A Systolic Array for SVD Updating

In an earlier paper, an approximate SVD updating scheme has been derived as an interlacing of a QR updating on the one hand and a Jacobi-type SVD procedure on the other hand, possibly supplemented with a certain re-orthogonali nation scheme. This paper maps this updating algorithm onto a systolic array with $O( n^2 )$ parallelism for $O( n^2 )$ complexity, resulting in an $O( n^0 )$ throughput. Furthermore, it is shown how a square root-free implementation is obtained by combining modified Givens rotations with approximate SVD schemes. In an earlier paper, an approximate SVD updating scheme has been derived as an interlacing of a QR updating on the one hand and a Jacobi-type SVD procedure on the other hand, possibly supplemented with a certain re-orthogonali nation scheme. This paper maps this updating algorithm onto a systolic array with $O( n^2 )$ parallelism for $O( n^2 )$ complexity, resulting in an $O( n^0 )$ throughput. Furthermore, it is shown how a square root-free implementation is obtained by combining modified Givens rotations with approximate SVD schemes.