A Systolic Array for SVD Updating

• Published in: SIAM journal on matrix analysis and applications Vol. 14; no. 2; pp. 353 - 371
• Main Authors: Moonen, Marc, Van Dooren, Paul, Vandewalle, Joos
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.04.1993
• Subjects: Algorithms; Decomposition; Exact sciences and technology; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Sciences and techniques of general use; Parallel algorithm; Least squares method; Recursive method; Matrix product; Updating; Systolic network; Factorization; Singular value decomposition
• ISSN: 0895-4798; 1095-7162
• DOI: 10.1137/0614025

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.