## A systolic architecture for the symmetric eigenvalue problem

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;
Report TR 82-525, DCS, Cornell University;
Report CMA-R03-82, CMA, ANU, August 1982, 23 pp.

## Abstract

An algorithm is presented for computing the eigenvalues and eigenvectors
of an *n* × *n* real symmetric matrix.
The algorithm is essentially a Jacobi method implemented on a
two-dimensional systolic array of O(*n*^{2}) processors
with nearest-neighbour communication between processors.
The speedup over the serial Jacobi method is of order
*n*^{2}, so the algorithm converges
to working accuracy in time O(*nS*), where
*S* is the number of sweeps.
## Comments

A revision of this Report is incorporated in
[84],
where it is conjectured
that *S*(*n*) = O(log *n*).
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