Numerically stable Jacobi array for parallel singular value decomposition (SVD) updating
Filiep J. Vanpoucke, Marc Moonen, Ed F. A. Deprettere · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
A novel algorithm is presented for updating the singular value decomposition in parallel. It is an improvement upon an earlier developed Jacobi-type SVD updating algorithm, where now the exact orthogonality of a certain matrix is guaranteed by means of a minimal factorization in terms of angles. Its orthogonality is known to be crucial for the numerical stability of the overall algorithm. The factored approach leads to a triangular array of rotation cells, implementing an orthogonal matrix-vector multiplication, and a novel array for SVD updating. Both arrays can be built up of CORDIC processors since the algorithms make exclusive use of orthogonal planar transformations.