Singular Value Decomposition With Systolic Arrays

Ilse Ipsen

doi:10.1117/12.944004

28 November 1984 Singular Value Decomposition With Systolic Arrays

Ilse Ipsen

Proceedings Volume 0495, Real-Time Signal Processing VII; (1984) https://doi.org/10.1117/12.944004
Event: 28th Annual Technical Symposium, 1984, San Diego, United States

Abstract

Systolic arrays for determining the Singular Value Decomposition of a mxn, m > n, matrix A of bandwidth w are presented. After A has been reduced to bidiagonal form B by means of Givens plane rotations, the singular values of B are computed by the Golub-Reinsch iteration. The products of plane rotations form the matrices of left and right singular vectors. Assuming each processor can compute or apply a plane rotation, 0(wn) processors accomplish the reduction to bidiagonal form in 0(np) steps, where p is the number of superdiagonals. A constant number of processors can then determine each singular value in about 6n steps. The singular vectors are computed by rerouting the rotations through the arrays used for the reduction to bidiagonal form, or else "along the way" by employing another rectangular array of O(wm) processors.

Citation Download Citation

Ilse Ipsen "Singular Value Decomposition With Systolic Arrays", Proc. SPIE 0495, Real-Time Signal Processing VII, (28 November 1984); https://doi.org/10.1117/12.944004

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