Proceedings PaperSingular Value Decomposition With Systolic Arrays
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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.