- This list is rather long. You may prefer the shorter list of selected publications.
- Please click on the appropriate title to obtain more information on that publication.
- For details of file formats, press here.
- Some bibliographic details are omitted here. Full details are available in pdf format.
- Reviews by Richard Brent are available separately.
- Selected abstracts are available in one file.
- Shortcuts: jump to year 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2015, end.

2. R. P. Brent,
* Algorithms for matrix multiplication*,
Report TR-CS-70-157, DCS, Stanford (March 1970). [Master's thesis.]

3. R. P. Brent,
On the addition of binary numbers,
* IEEE Transactions on Computers* C-19 (1970), 758-759.

4. R. P. Brent,
Error analysis of algorithms for matrix multiplication
and triangular decomposition using Winograd's identity,
* Numerische Mathematik* 16 (1970), 145-156.

5. R. P. Brent,
An algorithm with guaranteed convergence for finding
a zero of a function,
* Computer Journal* 14 (1971), 422-425.

6. R. P. Brent,
* Algorithms for finding zeros and extrema of
functions without calculating derivatives*,
Report TR CS 198, DCS, Stanford (February 1971). [Ph.D. thesis.]

7. R. P. Brent,
A new algorithm for minimizing a function of several
variables without calculating derivatives,
in * Optimization*,
University of Queensland Press, Brisbane, 1972, 14-25.

8. R. P. Brent,
On the Davidenko-Branin method for solving
simultaneous nonlinear equations,
* IBM J. Research and Development* 16 (1972), 434-436.

9. R. P. Brent,
A modified linear scatter storage technique,
* IBM Technical Disclosure Bulletin* 14 (1972), 3489.

10. R. P. Brent,
An optimal secant method for solving systems of
nonlinear equations,
* IBM Technical Disclosure Bulletin* 15 (1972), 1216-1217.

11. R. P. Brent,
* Algorithms for Minimization without Derivatives*,
Prentice-Hall, Englewood Cliffs, New Jersey, 1973, 195 pp.
Errata.

Reprinted by Dover, New York, 2002 and 2013.

12. R. P. Brent,
The computational complexity of iterative methods for
systems of nonlinear equations,
in * Complexity of Computer Computations*,
Plenum Press, New York, 1972, 61-71.

13. R. P. Brent,
Reducing the retrieval time of scatter storage techniques,
* Communications of the ACM* 16 (1973), 105-109.

14. R. P. Brent,
Some efficient algorithms for solving systems of nonlinear equations,
* SIAM J. Numerical Analysis* 10 (1973), 327-344.

15. R. P. Brent, D. J. Kuck and K. Maruyama,
The parallel evaluation of
arithmetic expressions without division,
* IEEE Transactions on Computers* C-22 (1973), 532-534.

16. R. P. Brent, S. Winograd and P. Wolfe,
Optimal iterative processes for rootfinding,
* Numerische Mathematik* 20 (1973), 327-341.

17. R. P. Brent,
On the precision attainable with various
floating-point number systems,
* IEEE Transactions on Computers* C-22 (1973), 601-607.

18. R. P. Brent,
The parallel evaluation of arithmetic expressions in
logarithmic time,
in * Complexity of Sequential and Parallel Numerical Algorithms*,
Academic Press, New York, 1973, 83-102.

19. R. P. Brent,
The first occurrence of large gaps
between successive primes,
* Mathematics of Computation* 27 (1973), 959-963.

20. R. P. Brent,
Sources of error in computation,
in * Error, Approximation and Accuracy*,
University of Queensland Press, Brisbane, 1973, 122-128.

21. R. P. Brent,
The distribution of small gaps
between successive primes,
* Mathematics of Computation* 28 (1974), 315-324.

22. R. P. Brent,
The parallel evaluation of general arithmetic
expressions,
* J. ACM* 21 (1974), 201-206.

23. R. P. Brent,
Algorithm 488: A Gaussian pseudo-random
number generator,
* Communications of the ACM* 17 (1974), 704-706.

24. R. P. Brent,
Irregularities in the distribution of primes
and twin primes,
* Mathematics of Computation* 29 (1975), 43-56.

25. R. P. Brent,
* Numerical solution of nonlinear equations*,
Dept. of Computer Science, Stanford University (March 1975),
189 pp.

26. R. P. Brent,
Some high-order zero-finding methods using almost orthogonal polynomials,
* J. Australian Mathematical Society (Series B)*
19 (1975), 1-29.

27. R. P. Brent,
A class of optimal-order zero-finding methods using derivative evaluations,
in * Analytic Computational Complexity*,
Academic Press, 1975, 59-73.

28. R. P. Brent,
Multiple-precision zero-finding methods and the complexity
of elementary function evaluation,
in * Analytic Computational Complexity*,
Academic Press, New York, 1975, 151-176.

29. R. P. Brent and H. T. Kung,
O((*n*
log *n*)^{3/2})
algorithms for composition and reversion of power series,
in * Analytic Computational Complexity*,
Academic Press, New York, 1975, 217-225.

30. J. P. Abbott and R. P. Brent,
Fast local convergence with single and
multistep methods for nonlinear equations,
* J. Australian Mathematical Society (Series B)*
19 (1975), 173-199.

31. R. S. Anderssen and R. P. Brent (editors),
* The Complexity of Computational Problem Solving*,
University of Queensland Press, Brisbane, 1976, 262 pp.

32. R. P. Brent, The complexity of multiple-precision arithmetic, in [31], 126-165.

33. R. S. Anderssen, R. P. Brent, D. J. Daley and P. A. P. Moran,
Concerning
and a Taylor series method,
* SIAM J. Applied Mathematics* 30 (1976), 22-30.

34. R. P. Brent,
Fast multiple-precision evaluation of elementary functions,
* J. ACM* 23 (1976), 242-251.

35. R. P. Brent,
* MP Users Guide (fourth edition)*,
TR-CS-81-08, Dept. of Computer Science, ANU (June 1981), 73 pp.

36. R. P. Brent,
* Knuth's constants to 1000 decimal and 1100 octal places*,
Report TR 47, Computer Centre, ANU (September 1975), 25 pp.

37. R. P. Brent,
Analysis of the binary Euclidean algorithm,
in * New Directions and Recent Results in Algorithms and Complexity*,
Academic Press, New York, 1976, 321-355.

38. R. Towle and R. P. Brent,
On the time required to parse an arithmetic
statement for parallel processing,
in * Proceedings of the 1976
International Conference on Parallel Processing*,
IEEE, New York, 1976, 254.

39. R. P. Brent and H. T. Kung,
Fast algorithms for composition
and reversion of multivariate power series,
in * Proceedings of a Conference on Theoretical Computer Science*,
Dept. of Computer Science, University of Waterloo,
Waterloo, Ontario (August 1977), 149-158.

40. R. P. Brent,
Computation of the regular continued fraction for Euler's constant,
* Mathematics of Computation* 31 (1977), 771-777.

41. A. H. Sameh and R. P. Brent,
Solving triangular systems on a parallel computer,
* SIAM J. Numerical Analysis* 14 (1977), 1101-1113.

42. R. P. Brent,
A Fortran multiple-precision arithmetic package,
* ACM Transactions on Mathematical Software* 4 (1978), 57-70.

43. R. P. Brent,
Algorithm 524: MP, a Fortran multiple-precision arithmetic package [A1],
* ACM Transactions on Mathematical Software* 4 (1978), 71-81.

44. J. P. Abbott and R. P. Brent,
A note on continuation methods for the solution of nonlinear equations,
* J. Australian Mathematical Society (Series B)*
20 (1978), 157-164.

45. R. P. Brent and H. T. Kung,
Fast algorithms for manipulating formal power series,
* J. ACM* 25 (1978), 581-595.

46. R. P. Brent *et al*,
Comments on the draft Pascal standard,
* Australian Computer Science Communications* 1 (1979), 310-317.

47. R. P. Brent,
On the zeros of the Riemann zeta function in the critical strip,
* Mathematics of Computation* 33 (1979), 1361-1372.

48. R. P. Brent and R. A. Jarvis (editors),
* Australian Computer Science Communications*
2, 1 (1980), 222 pp.

49. R. P. Brent and E. M. McMillan,
Some new algorithms for high-precision computation of Euler's constant,
* Mathematics of Computation* 34 (1980), 305-312.

50. R. P. Brent and J. F. Traub,
On the complexity of composition and
generalized composition of power series,
* SIAM J. Computing* 9 (1980), 54-66.

51. R. P. Brent,
An improved Monte Carlo factorization algorithm,
* BIT* 20 (1980), 176-184.

52. R. P. Brent,
Unrestricted algorithms for elementary and special functions,
in * Information Processing 80*,
North-Holland, Amsterdam, 1980, 613-619.

53. R. P. Brent and H. T. Kung,
The chip complexity of binary arithmetic,
* Proceedings of the Twelfth Annual ACM Symposium on the
Theory of Computing*,
ACM, New York, 1980, 190-200.

54. R. P. Brent, J. A. Hooper and J. M. Yohe,
An Augment interface for Brent's multiple-precision arithmetic package,
* ACM Transactions on Mathematical Software* 6 (1980), 146-149.

55. R. P. Brent and H. T. Kung,
The area-time complexity of binary multiplication,
* J. ACM* 28 (1981), 521-534.
Corrigendum: * ibid* 29 (1982), 904.

56. R. P. Brent and H. T. Kung,
On the area of binary tree layouts,
* Information Processing Letters* 11 (1980), 46-48.

57. R. P. Brent,
The first occurrence of certain large prime gaps,
* Mathematics of Computation* 35 (1980), 1435-1436.

58. G. M. Baudet, R. P. Brent and H. T. Kung,
Parallel execution of a
sequence of tasks on an asynchronous multiprocessor,
* Australian Computer Journal* 12 (1980), 105-112.

59. R. P. Brent, F. G. Gustavson and D. Y. Y. Yun,
Fast solution of Toeplitz systems of equations and computation of
Padé approximants,
* J. Algorithms* 1 (1980), 259-295.

60. R. P. Brent and H. T. Kung,
A regular layout for parallel adders,
* IEEE Transactions on Computers* C-31 (1982), 260-264.

61. R. P. Brent and J. M. Pollard,
Factorization of the eighth Fermat number,
* Mathematics of Computation* 36 (1981), 627-630.

62. R. P. Brent,
* Topics in computational complexity
and the analysis of algorithms*,
Report TR-CS-80-14, DCS, ANU, October 1980, 375 pp.
[D.Sc. thesis.]

63. R. P. Brent,
Comments on papers by Maddison and Westreich,
* Computer Journal* 24 (1981), 95-96.

64. R. P. Brent and L. M. Goldschlager,
Some area-time tradeoffs for VLSI,
* SIAM J. on Computing* 11 (1982), 737-747.

65. A. W. Bojanczyk, R. P. Brent and H. T. Kung,
Numerically stable solution
of dense systems of linear equations using mesh-connected processors,
* SIAM J. Scientific and Statistical Computing* 5 (1984), 95-104.

66. R. P. Brent,
Succinct proofs of primality for the factors of some Fermat numbers,
* Mathematics of Computation* 38 (1982), 253-255.

67. R. P. Brent,
New factors of Mersenne numbers (preliminary report),
* AMS Abstracts* 2 (1981), 367, 81T-10-246;
part II, * ibid *3 (1982), 132, 82T-10-22;
part III, * ibid *4 (1983), 197, 83T-10-138.

68. R. P. Brent,
Efficient implementation of the first-fit strategy for
dynamic storage allocation,
* Australian Computer Science Communications* 3 (1981), 25-34.

69. R. P. Brent,
An idealist's view of semantics for integer and real types,
* Australian Computer Science Communications* 4 (1982), 130-140.

70. R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter,
On the zeros of the Riemann zeta function in the critical strip, II,
* Mathematics of Computation* 39 (1982), 681-688.

71. R. P. Brent and R.R. Ewin,
Design of an nMOS parallel adder,
* AUSMPC Design Community Newsletter* 2 (August 1982), 1-14.

72. R. P. Brent and L. M. Goldschlager,
Area-time tradeoffs for VLSI circuits,
* Microelectronics '82*,
Institution of Engineers, Australia,
National Conference Publication # 82/4, April 1982, 52-56.

73. R. P. Brent and H. T. Kung,
Systolic VLSI arrays for polynomial GCD computation,
* IEEE Transactions on Computers* C-33 (1984), 731-736.

74. R. P. Brent and F. T. Luk,
Computing the Cholesky factorization using a systolic architecture,
* Proceedings of the Sixth Australian Computer Science Conference*,
special issue of * Australian Computer Science Communications* 5 (1983),
295-302.

75. R. P. Brent and F. T. Luk,
* A systolic architecture for the singular value decomposition*,
Report TR-CS-82-09, DCS, ANU.

76. R. P. Brent and F. T. Luk,
* A systolic architecture for almost
linear-time solution of the symmetric eigenvalue problem*,
Report TR-CS-82-10, DCS, ANU.

77. R. P. Brent and H. T. Kung,
A systolic VLSI array for integer GCD computation,
in * ARITH-7, Proceedings of the Seventh Symposium on
Computer Arithmetic*, IEEE CS Press, 1985, 118-125.

78. R. P. Brent and F. T. Luk,
A systolic array for the linear-time solution
of Toeplitz systems of equations,
* J. of VLSI and Computer Systems* 1, 1 (1983), 1-23.

79. R. P. Brent, H. T. Kung and F. T. Luk,
Some linear-time algorithms for systolic arrays,
in * Information Processing 83*,
North-Holland, Amsterdam, 1983, 865-876.

80. R. P. Brent, F. T. Luk and C. F. Van Loan,
Computation of the singular
value decomposition using mesh-connected processors,
* J. of VLSI and Computer Systems* 1, 3 (1983-1985), 242-270.
Also Report TR 82-528, DCS, Cornell University, Nov. 1982.

81. R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter,
The first 200,000,001 zeros of Riemann's zeta function,
in * Computational Methods in Number Theory*
(edited by H. W. Lenstra, Jr. and R. Tijdeman),
Mathematical Centre Tracts 154,
Mathematisch Centrum, Amsterdam, 1982, 389-403.

82. R. P. Brent and H. T. Kung,
Systolic VLSI arrays for linear-time GCD computation,
in * VLSI 83* (edited by F. Anceau and E. J. Aas),
North-Holland, Amsterdam, 1983, 145-154.

83. R. P. Brent, F. T. Luk and C. F. Van Loan,
Computation of the generalized
singular value decomposition using mesh-connected processors,
* Proceedings SPIE, Volume 431, Real Time Signal Processing VI*,
SPIE, Bellingham, Washington, 1983, 66-71.

84. R. P. Brent and F. T. Luk,
The solution of singular-value and symmetric
eigenvalue problems on multiprocessor arrays,
* SIAM J. Scientific and Statistical Computing* 6 (1985), 69-84.

85. R. P. Brent and L. M. Goldschlager,
A parallel algorithm for context-free parsing,
* Australian Computer Science Communications* 6 (1984), 7.1-10.

86. A. W. Bojanczyk and R. P. Brent,
Tridiagonalization of a symmetric matrix
on a square array of mesh-connected processors,
* J. Parallel and Distributed Computing* 2 (1985), 261-276.

87. R. P. Brent and F. T. Luk,
The solution of singular-value problems using systolic arrays,
* Proceedings SPIE, Volume 495,
Real Time Signal Processing VII*,
SPIE, Bellingham, Washington, 1984, 7-12.

88. A. W. Bojanczyk and R. P. Brent,
Parallel solution of certain Toeplitz least squares problems,
* J. Linear Algebra and its Applications* 77 (1986), 43-60.

89. R. P. Brent,
Efficient implementation of the first-fit strategy for
dynamic storage allocation,
* ACM Trans. on Programming Languages and Systems*
11, 3 (July 1989), 388-403.

90. R. P. Brent,
*Dynamic storage allocation on a computer with virtual memory*,
Report CMA-R37-84, CMA, ANU, September 1984;
Report TR-CS-84-06, DCS, ANU, October 1984, 42 pp.

91. R. P. Brent,
The most-recently-used strategy for dynamic storage
allocation on a computer with virtual memory,
* Australian Computer Science Communications* 7 (1985), 17.1-17.8.

92. A. W. Bojanczyk, R. P. Brent and F. R. de Hoog,
QR factorization of Toeplitz matrices,
* Numerische Mathematik* 49 (1986), 81-94.

93. A. W. Bojanczyk, R. P. Brent and F. R. de Hoog,
Linearly connected arrays for Toeplitz least squares problems,
* J. Parallel and Distributed Computing* 9 (1990), 261-270.

94. R. P. Brent and B. D. McKay,
Determinants and ranks of random matrices over
*Z*_{m} ,
*Discrete Mathematics* 66 (1987), 35-49.

95. A. W. Bojanczyk, R. P. Brent, P. Van Dooren and F. R. de Hoog,
A note on downdating the Cholesky factorization,
* SIAM J. Scientific and Statistical Computing* 8 (1987), 210-221.

96. A. W. Bojanczyk and R. P. Brent,
A systolic algorithm for extended GCD computation,
* Comput. Math. Applic. *14 (1987), 233-238.

97. R. P. Brent,
* Some integer factorization algorithms using elliptic curves*,
Report CMA-R32-85, CMA, ANU, September 1985, 20 pp.

98. R. P. Brent,
A linear algorithm for data compression,
* Australian Computer Journal* 19, 2 (May 1987), 64-68.

99. B. B. Zhou and R. P. Brent,
An efficient architecture for solving
the recursive convolution equation with high throughput,
* Proceedings of the First IASTED International Symposium on Signal
Processing and its Applications*
(edited by B. Boashash),
Institution of Engineers, Australia, Vol. 2, 1987, 771-775.

100. R. P. Brent and G. L. Cohen,
A new lower bound for odd perfect numbers,
* Mathematics of Computation* 53 (1989), 431-437.
Supplement, * ibid*, S7-S24.

101. R. P. Brent and B. D. McKay,
On determinants of random symmetric matrices over
*Z*_{m} ,
* Ars Combinatoria* 26A (1988), 57-64.

102. R. P. Brent,
Some integer factorization algorithms using elliptic curves,
* Australian Computer Science Communications* 8 (1986), 149-163.

103. B. B. Zhou and R. P. Brent,
A high throughput systolic implementation of the second order
recursive filter,
* Proceedings IEEE 1988 Conference
on Acoustics, Speech and Signal Processing*
(New York, April 1988), Volume 4, 2053-2056.

104. B. B. Zhou and R. P. Brent,
* A two-level pipelined implementation of direct-form
recursive filters*,
Report TR-CS-88-06, CSL, ANU, April 1988, 16 pp.

105. R. P. Brent and B. B. Zhou,
A stabilized parallel algorithm for direct-form recursive filters,
* IEEE Transactions on Computers* C-40, 3 (March 1991), 333-336.

106. R. P. Brent, G. L. Cohen and H. J. J. te Riele,
* A new approach to lower bounds for odd perfect numbers*,
Report TR-CS-88-08, CSL, ANU, August 1988, 71 pp.

107. T. Bossomaier and R. P. Brent,
Matrix diagonalisation by transputers,
* Proc. First Australian Transputer
and Occam Conference* (Melbourne, June 1988), 11-14.

108. R. P. Brent,
Old and new algorithms for Toeplitz systems,
* Proceedings SPIE, Volume 975,
Advanced Algorithms and Architectures for Signal Processing* III,
SPIE, Bellingham, Washington, 1989, 2-9.

109. C. J. Anfinson, R. P. Brent and F. T. Luk,
A theoretical foundation for the weighted checksum scheme,
* Proceedings SPIE, Volume 975,
Advanced Algorithms and Architectures for Signal Processing III*
SPIE, Bellingham, Washington, 1989, 10-18.

110. R. P. Brent,
Parallel algorithms for digital signal processing,
* Numerical Linear Algebra, Digital Signal Processing
and Parallel Algorithms*
Springer-Verlag, 1991, 93-110.

111. R. P. Brent,
Parallel algorithms for Toeplitz systems,
* Numerical Linear Algebra, Digital Signal Processing
and Parallel Algorithms*
Springer-Verlag, 1991, 75-92.

112. R. P. Brent, F. T. Luk and C. J. Anfinson,
Checksum schemes for fault tolerant systolic computing,
* Mathematics in Signal Processing II*,
Clarendon Press, Oxford, 1990, 791-804.

113. R. P. Brent,
Factorization of the eleventh Fermat number,
* AMS Abstracts* 10 (1989), 89T-11-73.

114. R. P. Brent, F. T. Luk and C. J. Anfinson,
Choosing small weights for multiple error detection,
* Proceedings SPIE, Volume 1058, High Speed Computing II*,
SPIE, Los Angeles, 1989, 130-136.

115. R. P. Brent,
Parallel algorithms for integer factorisation,
* Number Theory and Cryptography* (edited by J. H. Loxton),
London Mathematical Society Lecture Note Series 154,
Cambridge University Press, 1990, 26-37.

116. R. P. Brent, G. L. Cohen and H. J. J. te Riele,
Improved techniques for lower bounds for odd perfect numbers,
* Mathematics of Computation* 57 (1991), 857-868.

117. R. P. Brent,
* Factor: an integer factorization program for the IBM PC*,
Report TR-CS-89-23, October 1989, 7 pp.

118. R. P. Brent,
Factorising,
* Australian Mathematical Society Gazette*
16, 5 (1989), 154-155.

119. R. P. Brent,
Fast training algorithms for multi-layer neural nets,
* IEEE Transactions on Neural Networks* 2 (1991), 346-354.

120. R. P. Brent,
Primality testing and integer factorisation,
in * The Role of Mathematics in Science*,
Australian Academy of Science, 1991, 14-26.

121. P. E. Strazdins and R. P. Brent, Implementing BLAS level 3 on the CAP-II, in [123], 121-129.

122. R. P. Brent,
Vector and parallel algorithms for integer factorisation,
* Proceedings Third Australian Supercomputer Conference*
(Melbourne, December 1990), Strategic Research Foundation,
University of Melbourne, 12 pp.

123. R. P. Brent and M. Ishii (editors),
* Proceedings of the First Fujitsu-ANU CAP Workshop*,
Fujitsu Research Laboratories,
Kawasaki, Japan, November 1990, 205 pp.

124. D. L. Boley, R. P. Brent, G. H. Golub and F. T. Luk,
Algorithmic fault tolerance using the Lanczos method,
* SIAM J. Matrix Analysis and Applications* 13 (1992), 312-332.

125. R. P. Brent,
Parallel computers and parallel algorithms,
* Australian Computer Science Communications*
13, 1 (1991), 1.

126. A. W. Bojanczyk, R. P. Brent and F. R. de Hoog,
*Stability analysis of fast Toeplitz linear system solvers*,
Report CMA-MR17-91, CMA, ANU, August 1991, 18 pp.

127. R. P. Brent,
Computing Aurifeuillian factors,
in * Computational Algebra and Number Theory*,
Mathematics and its Applications, vol. 325,
Kluwer Academic Publishers, Boston, 1995, 201-212.

128. R. P. Brent,
Parallel algorithms in linear algebra,
* Algorithms and Architectures:
Proceedings of the Second NEC Research Symposium*
(held at Tsukuba, Japan, August 1991),
SIAM, Philadelphia, 1993, 54-72.

129. R. P. Brent (editor),
* Proceedings of the Second Fujitsu-ANU CAP Workshop*,
ANU, November 1991, 254 pp.

130. R. P. Brent,
The LINPACK benchmark on the AP1000,
* Proceedings of Frontiers '92*
(McLean, Virginia, October 1992), IEEE Press, 1992, 128-135.

131. P. E. Strazdins and R. P. Brent, The implementation of BLAS level 3 on the AP 1000: Preliminary report, in [129], H1-H17.

132. R. P. Brent,
Uniform random number generators for supercomputers,
* Proc. Fifth Australian Supercomputer Conference*,
Melbourne, December 1992, 95-104.

133. R. P. Brent,
On the periods of generalized Fibonacci recurrences,
* Mathematics of Computation* 63 (1994), 389-401.

134. R. P. Brent and H. J. J. te Riele,
*Factorizations* *of a*^{n}__+__ 1, 13 __<__ *a* < 100,
Report NM-R9212, Centrum voor Wiskunde en Informatica, Amsterdam,
June 1992, viii+363 pp.
Also (with P. L. Montgomery) various updates.

135. R. P. Brent,
On computing factors of cyclotomic polynomials,
* Mathematics of Computation* 61 (1993), 131-149
(D. H. Lehmer memorial issue).

136. R. P. Brent and P. E. Strazdins,
Implementation of the BLAS level 3 and Linpack benchmark on the AP1000,
* Fujitsu Scientific and Technical Journal* 29, 1 (1993),
61-70.

137. B. B. Zhou and R. P. Brent,
Parallel implementation of eigenvalue algorithms
on distributed memory machines,
* Australian Computer Science Communications* 15 (1993), 19-25.

138. B. B. Zhou and R. P. Brent,
Parallel computation of the singular value
decomposition on tree architectures,
* Proc. 22nd ICPP*,
CRC Press, Ann Arbor, 1993, Vol. 3, 128-131.

139. R. P. Brent,
Ramanujan and Euler's constant,
* Proceedings of Symposia in Applied Mathematics*, Vol. 48,
American Mathematical Society, Providence,
Rhode Island, 1994, 541-545.

140. R. P. Brent and A. Tridgell,
A fast, storage-efficient parallel sorting algorithm,
* Proceedings of the International Conference on
Application-Specific Array Processors*
(edited by L. Dadda and B. Wah), IEEE CS Press,
1993, 369-379.

141. R. P. Brent,
* Fast normal random number generators on vector processors,*
Technical Report TR-CS-93-04, CSL, ANU, March 1993, 6 pp.

142. B. B. Zhou, R. P. Brent and A. Tridgell,
Efficient implementation of
sorting algorithms on asynchronous distributed-memory machines,
* Proceedings of the 1994 International Conference on
Parallel and Distributed Systems*,
IEEE CS Press, 1994, 102-106.

143. A. W. Bojanczyk, R. P. Brent and F. R. de Hoog,
Stability analysis of a general Toeplitz system solver,
* Numerical Algorithms* 10 (1995), 225-244.

144. A. W. Bojanczyk, R. P. Brent, F. R. de Hoog and D. R. Sweet,
On the stability of the Bareiss and related Toeplitz
factorization algorithms,
* SIAM J. Matrix Analysis and Applications* 16 (1995), 40-57.

145. B. B. Zhou and R. P. Brent,
Parallel implementation of QRD algorithms on the Fujitsu AP1000,
* Australian Computer Science Communications* 16 (1994), 733-743.

146. R. P. Brent, A. Czezowski, M. Hegland, P. E. Strazdins and B. B. Zhou,
Linear algebra research on the AP1000,
* Proceedings of the Second Parallel Computing Workshop*,
Fujitsu Laboratories, Kawasaki, Japan,
Nov. 1993, P1-L1-13.

147. R. P. Brent,
* Uses of randomness in computation*,
Technical Report TR-CS-94-06,
CSL, ANU, June 1994, 14 pp.

148. R. P. Brent, A. J. Cleary, M. Hegland, J. H. Jenkinson,
Z. Leyk, M. Nakanishi, M. R. Osborne, P. J. Price, S. Roberts
and D. B. Singleton,
Implementation and performance of scalable scientific library subroutines
on Fujitsu's VPP500 parallel-vector supercomputer,
* Proceedings of the Scalable High Performance Computing Conference*,
IEEE CS Press, 1994, 526-533.

149. Hong Tang, B. B. Zhou, I. D. G. Macleod, R. P. Brent and Wei Sun,
Parallel implementation of an adaptive and iterative noise
filter for efficient signal restoration,
* Proc. TENCON 1994*,
Singapore, 1994, Vol. 2, 672-676.

150. R. P. Brent,
Integer Factorization,
in * Grand Challenges in Supercomputing at the Australian National
University*, CSL, ANU, April 1994, 34-39.

151. Hong Tang, B. B. Zhou, I. D. G. Macleod and R. P. Brent,
A class of parallel iterative median-type algorithms
for efficient image processing,
* Proc. ICSCI 1994,*
Wuhan, China, 1994, 21-28.

152. Hong Tang, B. B. Zhou, I. D. G. Macleod, R. P. Brent and Wei Sun,
Comparisons of parallel iterative noise filters for
real-time image processing,
* Proc. ICSPAT 1994*,
Dallas, Texas, 1994, Vol. 2, 1015-1020.

153. B. B. Zhou and R. P. Brent,
A parallel ring ordering algorithm
for efficient one-sided Jacobi SVD computations,
* J. Parallel and Distributed Computing* 42 (1997), 1-10.

154. B. B. Zhou and R. P. Brent,
On parallel implementation of the one-sided
Jacobi algorithm for singular value decompositions,
* Proceedings Euromicro Workshop on Parallel and
Distributed Processing*
(San Remo, Italy), IEEE CS Press, 1995, 401-408.

155. B. B. Zhou, R. P. Brent and M. H. Kahn,
Efficient one-sided Jacobi algorithms for singular value decomposition
and the symmetric eigenproblem,
* Proc. IEEE First International Conference on Algorithms and
Architectures for Parallel Processing*,
IEEE Press, 1995, 256-262.

156. C. Eldershaw and R. P. Brent,
Factorization of large integers on some vector and parallel computers,
* Proceedings of Neural, Parallel and Scientific Computations*
1 (1995), 143-148.

157. D. R. Sweet and R. P. Brent,
Error analysis of a fast partial pivoting method for structured matrices,
* Proceedings SPIE, Volume 2363, Advanced Signal Processing Algorithms*,
SPIE, Bellingham, Washington, 1995, 266-280.

158. A. Tridgell and R. P. Brent,
A general-purpose parallel sorting algorithm,
* International J. of High Speed Computing*
7 (1995), 285-301.
Also
A. Tridgell, R. P. Brent and B. D. McKay,
* Parallel Integer Sorting*,
Internal Report, DCS, ANU, December 1995.

159. B. B. Zhou and R. P. Brent,
Jacobi-like algorithms for eigenvalue decomposition of a
real normal matrix using real arithmetic,
* Australian Computer Science Communications* 18, 1 (1996), 367-375.

160. W. Ma, C. W. Johnson and R. P. Brent,
Concurrent programming in T-Cham,
* Australian Computer Science Communications* 18, 1 (1996), 291-300.

161. R. P. Brent,
Factorization of the tenth Fermat number,
* Mathematics of Computation* 68 (1999), 429-451.

162. W. Liang and R. P. Brent,
Constructing the spanners of graphs in parallel,
* Proceedings of the Tenth International Parallel Processing Symposium*
(IPPS '96), IEEE CS Press, 1996, 206-210.

163. B. B. Zhou and R. P. Brent,
Jacobi-like algorithms for eigenvalue decomposition of a real normal matrix
using real arithmetic,
* Proceedings of the Tenth International Parallel Processing Symposium*,
IEEE CS Press, 1996, 593-600.

164. W. Ma, C. W. Johnson and R. P. Brent,
Programming with transactions and the Chemical Abstract Machine,
* Proceedings of the 1996 International Symposium on Parallel Architectures, Algorithms,
and Networks*,
IEEE CS Press, 1996, 562-564.

165. J. Yang, W. Ma and R. P. Brent,
From hypertext to flat text: a tool for document construction,
* Proceedings of the Second Australian World Wide Web Conference*,
Southern Cross University Press, 1996, 67-72.

166. R. P. Brent, A. J. van der Poorten and H. J. J. te Riele,
A comparative study of algorithms for computing continued fractions of
algebraic numbers,
* Lecture Notes in Computer Science*, Vol. 1122, Springer-Verlag,
Berlin, 1996, 35-47.

167. B. B. Zhou, R. P. Brent and X. Qu,
The design of a supporting environment for online parallel debugging,
* Proceedings of the Sixth Parallel Computing Workshop*,
Kawasaki, Japan, November 1996, P1-S-1 -8.

168. B. B. Zhou, R. P. Brent, X. Qu and W. Liang,
A novel parallel algorithm for enumerating combinations,
* Proceedings of the 25th International Conference on
Parallel Processing*,
Bloomingdale, Illinois, August 1996.
IEEE Press, Vol. 2, 70-73.

169. B. B. Zhou, R. P. Brent and X. Qu,
An efficient scheduling algorithm for multiprogramming on parallel
computing systems,
* Australian Computer Science Communications* 19, 1 (1997), 336-345.

170. R. P. Brent,
* A fast vectorised implementation of Wallace's
normal random number generator*,
Technical Report TR-CS-97-07, CSL, ANU, April 1997, 9 pp.

171. M. Manzur Murshed and R. P. Brent,
* RMSIM: a serial simulator for
reconfigurable mesh parallel computers*,
Technical Report TR-CS-97-06, CSL, ANU, April, 1997, 10 pp.

172. X. Qu, J. X. Yu and R. P. Brent,
A mobile TCP socket,
* Proc. IASTED 1997*
(San Francisco, Nov. 1997), 5 pp.

173. R. P. Brent,
Numerical stability of some fast algorithms for structured matrices,
* Proceedings of the of the Sixth Workshop on Scientific Computing*
(Hong Kong, March 1997), Springer-Verlag, 1998, 41-48.

174. M. Manzur Murshed and R. P. Brent,
Constant time algorithms for computing the contour of maximal elements
on the reconfigurable mesh,
* Parallel Processing Letters* 8 (1998), 351-361.

175. R. P. Brent, R. E. Crandall, K. Dilcher and C. Van Halewyn,
Three new factors of Fermat numbers,
* Mathematics of Computation* 69 (2000), 1297-1304.

176. M. Manzur Murshed and R. P. Brent,
Algorithms for optimal self-simulation of some restricted reconfigurable
meshes,
* Proc. Second International Conference on Computational Intelligence and
Multimedia Applications* (Monash Univ., 1998),
World Scientific, Singapore, 1998, 734-744.

177. R. P. Brent,
Stability of fast algorithms for structured linear systems,
in * Fast Reliable Algorithms for Matrices with Structure*,
SIAM, Philadelphia, 1999, 103-116.

178. B. A. Murphy and R. P. Brent,
On quadratic polynomials for the number field sieve,
* Australian Computer Science Communications* 20, 3 (1998), 199-213.

179. X. Qu, J. X. Yu and R. P. Brent,
Implementation of a portable-IP system for mobile TCP/IP,
* Australian Computer Science Communications* 20, 1 (1998), 499-510.

180. B. B. Zhou, X. Qu and R. P. Brent,
Effective scheduling in a mixed parallel and
sequential computing environment,
* Proc. 6th Euromicro Workshop on Parallel and
Distributed Computing*, Madrid, Jan. 1998, 32-37.

181. B. B. Zhou, R. P. Brent, D. Walsh and K. Suzaki,
Job scheduling strategies for networks of workstations,
* Lecture Notes in Computer Science*, Vol. 1459,
Springer-Verlag, 1998, 143-157.

182. R. P. Brent * et al*,
Development of a mathematical subroutine library for Fujitsu
vector parallel processors,
* Proc. ACM International Conference on Supercomputing*,
Melbourne, July 1998, 13-20.

183. R. P. Brent,
Twenty years' analysis of the binary Euclidean algorithm,
* Millennial Perspectives in Computer Science*,
Palgrave, 2000, 41-53.

Also (extended version)
arXiv:1303.2772v1, 12 March 2013.

184. M. Manzur Murshed and R. P. Brent,
Serial simulation of reconfigurable mesh,
an image understanding architecture,
in * Advances in Computer Cybernetics*, Volume V, 1998, 92-97.

185. R. P. Brent,
Random number generation and simulation on vector and parallel
computers,
* Lecture Notes in Computer Science*, Vol. 1470,
Springer-Verlag, Berlin, 1998, 1-20.

186. M. Manzur Murshed and R. P. Brent,
Adaptive AT^{2}
optimal algorithms on reconfigurable meshes,
* J. Parallel Computing* 26 (2000), 1447-1458.

187. R. P. Brent * et al*,
Design of the scientific subroutine library for the Fujitsu VPP300,
* Proc. Third HPC Asia Conference*, Singapore, Sept. 1998,
424-438.

188. R. P. Brent,
Computer arithmetic - a programmer's perspective,
* Proc. ARITH 14*,
IEEE CS Press, 1999, 2.

189. B. B. Zhou, R. P. Brent, C. W. Johnson and D. Walsh,
Job re-packing for enhancing the performance of gang scheduling,
* Lecture Notes in Computer Science*, Vol. 1659 (1999), 129-143.

190. M. Manzur Murshed and R. P. Brent,
Maximal contour algorithms on constrained reconfigurable meshes,
* Proc. 1999 International Conference on Parallel and Distributed
Processing Techniques and Applications*,
CSREA Press, Vol. 4, 1999, 2238-2244.

191. M. Manzur Murshed and R. P. Brent,
A new adaptive sorting algorithm on the reconfigurable mesh,
an image understanding architecture,
in * Advances in Intelligent Computation and Multimedia Systems*,
IIASSRC, 1999, 183-188.

192. B. B. Zhou and R. P. Brent,
Gang scheduling with a queue for large jobs,
* Proc. IPDPS2001*, San Francisco, April 2001.

193.
R. P. Brent,
Some parallel algorithms for integer factorisation,
* Lecture Notes in Computer Science*, Vol. 1685,
Springer-Verlag, Berlin, 1999, 1-22.

194. B. B. Zhou, P. Mackerras, C. W. Johnson, D. Walsh and R. P. Brent,
An efficient resource allocation scheme for gang scheduling,
* Proc. IEEE International Workshop on Cluster Computing*
(Melbourne, 1999), 187-194.

195. M. Manzur Murshed and R. P. Brent,
How promising is the *k*-constrained reconfigurable mesh ?,
*Proc. 15th ISCA International Conference on
Computers and their Applications*
(New Orleans, March 2000), 9 pp.

196. R. P. Brent,
Recent progress and prospects for integer factorisation algorithms,
*Lecture Notes in Computer Science*, Vol. 1858,
Springer-Verlag, Berlin, 2000, 3-22.

197. R. P. Brent,
*Public key cryptography with a group of unknown order*,
Report PRG-TR-02-00, Oxford University Computing Laboratory, June 2000,
11 pp.

198. B. B. Zhou, D. Walsh and R. P. Brent,
Resource allocation schemes for gang scheduling,
*Lecture Notes in Computer Science*, Vol. 1911, 2000, 74-86.

199. R. P. Brent, S. Larvala and P. Zimmermann,
A fast algorithm for testing reducibility of trinomials mod 2
and some new primitive trinomials of degree 3021377,
* Mathematics of Computation* 72 (2003), 1443-1452.

200. R. P. Brent, P. Montgomery and H. te Riele,
*Factorizations of Cunningham numbers with bases 13 to 99:
Millennium edition*,
Report PRG TR-14-00, December 2000, vi+463 pp.

201. R. P. Brent, S. Gao and A. G. B. Lauder,
Random Krylov spaces over finite fields,
*SIAM Journal on Discrete Mathematics* 16 (2003), 276-287.

202. B. B. Zhou and R. P. Brent,
On the development of an efficient coscheduling system,
*Lecture Notes in Computer Science*, Vol. 2221, 2001, 103-115.

203. L. T. Yang and R. P. Brent,
Quantitative performance analysis of the improved quasi-minimal residual method
on massively distributed memory computers,
* Advances in Engineering Software* 33 (2002), 169-177.

204. W. Liang, R. P. Brent and H. Shen,
Fully dynamic maintenance of *k*-connectivity in parallel,
* IEEE Transactions on Parallel and Distributed Systems*
12 (2001), 846-864.

205. L. T. Yang and R. P. Brent,
Parallel execution time analysis for least squares problems on
distributed memory architectures,
* International Journal of Computer Research* 10, 4 (2001), 517-530.

206. L. T. Yang and R. P. Brent,
The improved BiCGStab method for large and sparse unsymmetric linear systems
on parallel distributed memory architectures,
* Proceedings of the Fifth International Conference on
Algorithms and Architectures for Parallel Processing (ICA3PP-02)*,
Beijing, October 2002, 324-328.

207. B. B. Zhou and R. P. Brent,
An efficient method for computing eigenvalues of a real normal matrix,
* Journal of Parallel and Distributed Computing* 63 (2003), 638-648.

208. L. T. Yang and R. P. Brent,
The improved parallel BiCG method for large and sparse linear systems on
parallel distributed memory architectures,
* Information Journal* 6 (2003), 349-360.

209. B. B. Zhou,
A. M. Goscinski and R. P. Brent,
Concerning the length of time slots for efficient gang scheduling,
*IEICE Transactions on Information and Systems* E86-D (2003), 1594-1600.

210. L. T. Yang and R. P. Brent,
The improved conjugate gradient squared (ICGS) method on parallel
distributed memory architectures,
* Workshop Proceedings of the 2001 International Conference on Parallel
Processing* (ICPP-HPSECA01), Valencia, Spain, September 2001, 161-165.

211. R. P. Brent and P. Zimmermann,
Random number generators with period divisible by a Mersenne prime,
*Computational Science and
its Applications - ICCSA 2003*,
* Lecture Notes in Computer Science*, Vol. 2667,
Springer-Verlag, Berlin, 2003, 1-10.

212. R. P. Brent and P. Zimmermann,
Algorithms for finding almost irreducible and almost primitive trinomials,
in * Primes and Misdemeanours: Lectures in Honour of the Sixtieth
Birthday of Hugh Cowie Williams*,
Fields Institute Communication FIC/41,
The Fields Institute, Toronto, 2004, 91-102.

213. R. P. Brent,
Some comments on C. S. Wallace's random number generators,
* Computer Journal* 51, 5 (Sept. 2008), 579-584.

214. R. P. Brent, S. Larvala and P. Zimmermann,
A primitive trinomial of degree 6972593,
* Mathematics of Computation* 74 (2005), 1001-1002.

215. L. T. Yang and R. P. Brent,
Improved Krylov subspace methods for large and sparse linear systems
on BSP architectures,
* Proc. IPDPS03*, IEEE Computer Society, 2003, 260b.

216. L. T. Yang and R. P. Brent,
Parallel MCGLS and ICGLS methods for least squares problems on distributed
memory architectures,
* The Journal of Supercomputing*, 29 (2004), 145-156.

217. R. P. Brent,
Fast and reliable random number generators for scientific computing,
* Proceedings of the PARA'04 Workshop on the
State-of-the-Art in Scientific Computing*,
Lyngby, Denmark, June 2004; *Lecture Notes in Computer Science*,
Vol. 3732 (2006), 1-10.

218. R. P. Brent,
Note on Marsaglia's xorshift random number generators,
* J. of Statistical Software* 11, 5 (2004), 1-4.

219. R. P. Brent,
Brain drain: a more positive note,
* Australian Mathematical Society Gazette* 31, 4 (2004), 234-238.

220. B. B. Zhou, M. Tarawneh, C. Wang, A. Zomaya and R. P. Brent,
A novel quartet-based method for phylogenetic inference,
*Proc. Fifth IEEE Symposium on Bioinformatics and Bioengineering*
(BIBE05), Minnesota, 19-21 Oct 2005, 32-39.

221. R. P. Brent, C. Percival and P. Zimmermann,
Error bounds on complex floating-point multiplication,
*Mathematics of Computation* 76 (2007), 1469-1481.

222. B. B. Zhou, D. Chu, M. Tarawneh, P. Wang, C. Wang,
A. Y. Zomaya and R. P. Brent,
Parallel implementation of a quartet-based algorithm for phylogenetic
analysis,
*Proceedings of the Fifth IEEE International Workshop on High Performance
Computational Biology* (HiCOMB06), Rhodes, Greece, April 2006, 8 pp.

223. B. B. Zhou, M. Tarawneh, D. Chu, P. Wang, C. Wang,
A. Y. Zomaya and R. P. Brent,
On a new quartet-based phylogeny reconstruction algorithm,
* Proceedings 2006 International Conference on
Bioinformatics and Computational Biology*
(BIOCOMP06), Las Vegas, USA, June 2006, 87-93.

224. R. P. Brent,
Some long-period random number generators using shifts and xors,
*ANZIAM Journal* 48 (CTAC2006), C188-C202, 2007.

225. R. P. Brent,
Fast algorithms for high-precision computation of elementary functions
(invited talk),
*Seventh Conference on Real Numbers and Computers*
(RNC7),
Nancy, France, 10-12 July 2006, 7-8 (extended abstract).

226. R. P. Brent and P. Zimmermann,
* Modern Computer Arithmetic*,
Cambridge University Press, 2010.

227. B. B. Zhou, M. Tarawneh, D. Chu, P. Wang, C. Wang, A. Zomaya
and R. P. Brent,
Evidence of multiple maximum likelihood points for a phylogenetic tree,
*Proc. Sixth IEEE Symposium on Bioinformatics and Bioengineering*
(BIBE06), Arlington, Virginia, Oct 2006, 193-197.

228. P. Wang, B. B. Zhou, M. Tarawneh, D. Chu, C. Wang, A. Zomaya
and R. P. Brent,
A global maximum likelihood super-quartet phylogeny method,
*Proc. Fifth Asia-Pacific Bioinformatics Conference*
(APBC2007), Hong Kong, Jan. 2007, 111-120.

229. Y. J. Lui, R. P. Brent and A. Calinescu,
Extracting significant phrases from text,
* Proc. 21st International Conference on Advanced Information
Networking and Applications* (AINA 2007),
Workshop Proceedings (AINAW07),
Vol. 1, May 2007, 361-366.

230. R. P. Brent and P. Zimmermann,
A multi-level blocking distinct-degree factorization algorithm,
in *Finite Fields and Applications: Contemporary Mathematics*, Vol. 461, 2008, 47-58.

231. Shi Bai and R. P. Brent,
On the efficiency of Pollard's rho method for discrete logarithms,
* The Australasian Theory Symposium* (CATS2008),
Wollongong, Jan. 2008.
*Conferences in Research and
Practice in Information Technology*, Vol. 77, edited by James Harland and
Prabhu Manyem, Australian Computer Society, 2008, 125-131.

232. R. P. Brent. P. Gaudry, E. Thomé and P. Zimmermann,
Faster multiplication in GF(2)[*x*],
* Proc. ANTS-VIII* (Banff, 17-22 May, 2008),
* Lecture Notes in Computer Science*, Vol. 5011,
Springer-Verlag, 2008, 153-166.
Also INRIA Tech Report RR-6359, Nov. 2007, 19 pp.

233. R. P. Brent and P. Zimmermann,
Ten new primitive binary trinomials,
* Mathematics of Computation* 78 (2009), 1197-1199.

234. W. Liang, R. P. Brent, Y. Xu and Q. Wang,
Minimum-energy all-to-all multicasting in wireless * ad hoc*
networks,
* IEEE Transactions on Wireless Communications* 8 (2009), 5490-5499.

235. R. P. Brent and P. Zimmermann,
The great trinomial hunt,
* Notices of the American Mathematical Society* 58, 2 (2011), 233-239.
Also
* Mathematical Advances in Translation* (Chinese)
33, 3 (2014), 248-257.

236. R. P. Brent and P. Zimmermann,
An *O(M(n)* log *n)* algorithm for the Jacobi symbol,
* Proc. ANTS-IX* (Nancy, 19-23 July 2010),
*Lecture Notes in Computer Science*, Vol. 6197,
Springer-Verlag, 2010, 83-95.

237. R. P. Brent, Note on computing ratings from eigenvectors, 5 May 2010, 10 pages, arXiv:1005.0762v1.

238. R. P. Brent, George Forsythe's last paper, 6 May 2010, 10 pages, arXiv:1005.0909v2.

239. R. P. Brent, A simple approach to error reconciliation in quantum key distribution, 7 May 2010, 19 pages, arXiv:1005.1206v1.

240. R. P. Brent, The myth of equidistribution for high-dimensional simulation, 8 May 2010, 8 pages. arXiv:1005.1320v1.

241. N. Nandapalan, R. P. Brent, L. M. Murray and A. Rendell,
High-performance pseudo-random number generation on graphics processing
units,
* Parallel Processing and Applied Mathematics*
(Proc. PPAM 2011, Torun, Poland, 11-14 Sept. 2011),
LNCS, Vol. 7203 (2012), 609--618.
arXiv:1108.0486v1.

242. R. P. Brent and D. Harvey,
Fast computation of Bernoulli, Tangent and Secant numbers,
* Proceedings of a Workshop on Computational and Analytical Mathematics
in honour of Jonathan Borwein's 60th birthday*, Springer Proceedings
in Mathematics and Statistics,
Vol. 50, 2013, 127-142.
arXiv:1108.0286v3.

243. L-T. Wang, N. A. Touba, R. P. Brent, H. Wang and H. Xu,
* High-speed Hybrid Ring Generator Design Providing Maximum-Length
Sequences with Low Hardware Cost*,
Tech. Report UT-CERC-12-01, Computer Engineering Research Center,
The University of Texas at Austin, USA, 4 Oct 2011, 12 pp.

244. R. P. Brent, J. Osborn, W. Orrick and P. Zimmermann, Maximal determinants and saturated D-optimal designs of orders 19 and 37, arXiv:1112.4160v1, 18 Dec 2011, 28 pp.

245. R. P. Brent,
Finding D-optimal designs by randomised decomposition and switching,
* Australasian Journal of Combinatorics*
55 (2013), 15-30.
arXiv:1112.4671v5.
Erratum.

246. J. Arias de Reyna, R. P. Brent and J. van de Lune,
A note on the real part of the Riemann zeta-function,
in
*Herman J. J. te Riele Liber Amicorum*,
CWI, Amsterdam, Dec. 2011, 30-36.
Errata:
arXiv:1112.4910v2.

247. R. P. Brent and J. van de Lune,
A note on Pólya's observation concerning Liouville's function,
in
*Herman J. J. te Riele Liber Amicorum*,
CWI, Amsterdam, Dec. 2011, 92-97.
arXiv:1112.4911v1.

248. J. Arias de Reyna, R. P. Brent and J. van de Lune,
On the sign of the real part of the Riemann zeta-function,
* Number Theory and Related Fields (in memory of
Alf van der Poorten)*,
Springer Proceedings in Mathematics and Statistics,
vol. 43,
Springer, New York, 2013, 75-97.
arXiv:1205.4423v2.

249. R. P. Brent and J. H. Osborn,
General lower bounds on maximal determinants of binary matrices,
* The Electronic Journal of Combinatorics* 20(2), 2013, #P15,
12 pp.
arXiv:1208.1805v6.

250. R. P. Brent and J. H. Osborn,
Bounds on minors of binary matrices,
* Bulletin of the Australian Math. Soc.* 88 (2013), 280-285.
Longer version:
arXiv:1208.3330v3,
9 pp.

251. R. P. Brent and J. H. Osborn,
On minors of maximal determinant matrices,
* Journal of Integer Sequences*, 16 (2013), article 13.4.2, 30 pp.

Also arXiv:1208.3819v3,
10 March 2013.

252. R. P. Brent,
Old and new algorithms for pi,
*Notices of the AMS* (letter to the editor) 60, 1 (Jan. 2013), 7.
arXiv:1303.2762v1.
[The relevant extract from Gauss's notebook entry of May 1809 is reproduced
here,
courtesy of Jörg Arndt.]

253. R. P. Brent, J. H. Osborn and W. D. Smith, Lower bounds on maximal determinants of +-1 matrices via the probabilistic method, 5 May 2013, 32 pp. arXiv:1211.3248v3.

254. Shi Bai, R. P. Brent and E. Thomé,
Root optimization of polynomials in the number field sieve,
* Mathematics of Computation* 84 (2015), 2447-2457.
Also arXiv:1211.1958v1.

255. R. P. Brent and J. H. Osborn, Note on a double binomial sum relevant to the Hadamard maximal determinant problem, 12 Sept. 2013, 6 pp. arXiv:1309.2795v2.

256. R. P. Brent and F. Johansson,
A bound for the error term in the Brent-McMillan algorithm,
* Mathematics of Computation* 84 (2015), 2351-2359.
Erratum and additional references.
Also arXiv:1309.0039v1.

257. R. P. Brent, J. H. Osborn and W. D. Smith, Lower bounds on maximal determinants of binary matrices via the probabilistic method, 25 October 2016, 37 pp. arXiv:1402.6817v6. For a shorter version see #262 below.

258. R. P. Brent, J. H. Osborn and Warren D. Smith,
Note on best possible bounds for determinants of matrices close to
the identity matrix,
* Linear Algebra and its Applications *
466 (2015), 21-26.
Also (longer version)
Bounds on determinants of perturbed diagonal matrices,
27 Mar. 2014, 18pp.
arXiv:1401.7084v7.

259. R. P. Brent,
Generalizing Tuenter's binomial sums,
*Journal of Integer Sequences* 18 (2015), article 15.3.2, 9 pp.
Also (longer version)
arXiv:1407.3533v4,
19 Jan. 2015, 17pp.

260. R. P. Brent, H. Ohtsuka, J. H. Osborn and H. Prodinger,
Some binomial sums involving absolute values,
*Journal of Integer Sequences* 19 (2016), article 16.3.7, 14 pp.
Also
arXiv:1411.1477v2,
31 Jan. 2016.

261. R. P. Brent, M. Coons and W. Zudilin,
Algebraic independence of Mahler functions via radial asymptotics,
* International Mathematics Research Notices*
2016:2 (2016), 571-603.
Also arXiv:1412.7906v2.

262. R. P. Brent, J. H. Osborn and W. D. Smith,
Probabilistic lower bounds on maximal determinants of binary matrices,
* Australasian Journal of Combinatorics* 66 (2016), 350-364.
Also (slightly revised version)
arXiv:1501.06235v7.
For a longer version see #257 above.

263. R. P. Brent, C. Krattenthaler and S. O. Warnaar,
Discrete analogues of Macdonald-Mehta integrals,
* J. Combinatorial Theory Series A* 144 (2016), 80-138.
Also arXiv:1601.06536v1.

264. R. P. Brent, A. Kruppa and P. Zimmermann,
FFT extension for algebraic-group factorization algorithms,
chapter 8
in
*Topics in Computational Number Theory inspired by
Peter L. Montgomery*, J. Bos and A. Lenstra (editors),
Cambridge University Press, 189-205, 2017.
Also hal-0163097.

265. D. H. Bailey, J. M. Borwein, R. P. Brent and M. Reisi Ardali,
Reproducibility in computational science: a case study: Randomness
of the digits of pi,
*Experimental Mathematics* 26 (2017), 298-305.
DOI: 10.1080/10586458.2016.1163755

266. R. P. Brent and P. Zimmermann, Twelve new primitive binary trinomials, 24 May 2016, arXiv:1605.09213v1.

267. R. P. Brent, Asymptotic approximation of central binomial coefficients with rigorous error bounds, 15 Sept. 2016, arXiv:1608.04834v2.

268. R. P. Brent,
On asymptotic approximations to the log-Gamma and Riemann-Siegel theta
functions,
* Journal of the Australian Mathematical Society*,
published online 21 Dec. 2018.
Also arXiv:1609.03682v2.

269. R. P. Brent,
The Borwein brothers, pi and the AGM,
* Proceedings of the Jonathan Borwein Commemorative Conference*
(edited by Brailey Sims), Springer, in press.
Also
arXiv:1802.07558v2.

270. R. P. Brent and A. B. Yedidia,
Computation of maximal determinants of binary circulant matrices,
*Journal of Integer Sequences* 21 (2018), article 18.5.6, 19 pp.
Updated version:
arXiv:1801.00399v5,
11 June 2019.

271. R. P. Brent, M. L. Glasser and A. J. Guttmann,
A conjectured integer sequence arising from the exponential integral,
*Journal of Integer Sequences* 22 (2019), article 19.4.7, 16 pp.
Also arXiv:1812.00316v4,
31 May 2019.

272. R. P. Brent, C. Pomerance, D. Purdum and J. Webster, Algorithms for the multiplication table, 12 August 2019, arXiv:1908.04251v1.

Return to Richard Brent's index page

Best viewed with a browser (any browser)