Richard Brent - Selected Publications

2. R. P. Brent, Algorithms for matrix multiplication, Report TR-CS-70-157, DCS, Stanford (March 1970), 52 pp.

11. R. P. Brent, Algorithms for minimization without derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, 1973, 195 pp. Reprinted by Dover, New York, 2002 and 2013.

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

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.

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, Journal of the ACM 21 (1974), 201-206.

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

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

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.

32. R. P. Brent, The complexity of multiple-precision arithmetic, in The Complexity of Computational Problem Solving, University of Queensland Press, Brisbane, 1976, 126-165.

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

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

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

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

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.

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

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

59. R. P. Brent, F. G. Gustavson and D. Y. Y. Yun, Fast solution of Toeplitz systems of equations and computation of Padé approximants, Journal of 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.

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.

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.

89. R. P. Brent, Efficient implementation of the first-fit strategy for dynamic storage allocation, ACM Transactions on Programming Languages and Systems 11 (1989), 388-405.

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

101. R. P. Brent and B. D. McKay, On determinants of random symmetric matrices over Zm, 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.

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.

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

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

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

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

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.

158. A. Tridgell and R. P. Brent, A general-purpose parallel sorting algorithm, International J. of High Speed Computing 7 (1995), 285-301.

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

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, in Algorithmic Number Theory (Henri Cohen, editor), Lecture Notes in Computer Science, Vol. 1122, Springer-Verlag, Berlin, 1996, 35-47.

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.

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.

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

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

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.

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

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.

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.

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.

212. R. P. Brent and P. Zimmermann, Algorithms for finding almost irreducible and almost primitive trinomials, Proceedings of a Conference in Honour of Professor H. C. Williams, Banff, Canada (May 2003), The Fields Institute, Toronto, 2004, 91-102.

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

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

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

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

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

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.

232. R. P. Brent. P. Gaudry, E. Thomé and P. Zimmermann, Faster multiplication in GF(2)[x], Proc. ANTS-VIII (Banff, May 17-22, 2008), edited by A. J. van der Poorten and A. Stein, Lecture Notes in Computer Science, Vol. 5011, Springer-Verlag, 2008, 153-166.

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

235. R. P. Brent and P. Zimmermann, The great trinomial hunt, Notices of the American Mathematical Society 58, 2 (2011), 233-239.

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.

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

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.

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.

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.

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. arXiv:1208.3819v3.

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.

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.

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. (Appeared electronically 16 Oct. 2014.)

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.

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.

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.

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

268. R. P. Brent, On asymptotic approximations to the log-Gamma and Riemann-Siegel theta functions, 6 Oct. 2016, arXiv:1609.03682v2.

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