Heath, M. T.; Laub, A. J.; Paige, C. C.; Ward, R. C. Computing the singular value decomposition of a product of two matrices. (English) Zbl 0607.65013 SIAM J. Sci. Stat. Comput. 7, 1147-1159 (1986). An algorithm for computing the singular value decomposition (SVD) of a product of two general matrices is given. SVD of an \(m\times n\) matrix A has the form \(A=U\Sigma V^ T\), where U and V are orthogonal matrices of order m and n respectively, and \(\Sigma\) is an \(m\times n\) nonnegative diagonal matrix. The algorithm is based on a Jacobi-like method due to Kogbetliantz and it is described in detail. The authors develop the basic method by using plane rotations applied to the two matrices separately. A triangular variant to compute the SVD is also given. The paper concludes with a discussion of implementation details and some test results. Reviewer: D.Herceg Cited in 1 ReviewCited in 36 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices Keywords:numerical examples; singular value decomposition; Jacobi-like method; Kogbetliantz; plane rotations Software:EISPACK PDFBibTeX XMLCite \textit{M. T. Heath} et al., SIAM J. Sci. Stat. Comput. 7, 1147--1159 (1986; Zbl 0607.65013) Full Text: DOI