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• W2030717234 abstract "We present a new algorithm for floating-point computation of the singular value decomposition (SVD) of the product $B^{tau}C$, where B and C are full row rank matrices. The algorithm replaces the pair $(B,C)$ with an equivalent pair $(B',C')$ and then it uses the Jacobi SVD algorithm to compute the SVD of the explicitly computed matrix $B'^{tau}C'$. In this way, each nonzero singular value $sigma$ is approximated with some $sigma+deltasigma$, where the relative error $|deltasigma|/sigma$ is, up to a factor of the dimensions, of order boldmath${varepsilon}$unboldmath ${min_{Deltain{cal D}}kappa_2(Delta B)+ min_{Deltain{cal D}} kappa_2(Delta C)}$, where ${cal D}$ denotes the set of diagonal nonsingular matrices, $kappa_2(cdot)$ denotes the spectral condition number, and boldmath${varepsilon}$unboldmath is the roundoff unit of floating-point arithmetic. The new algorithm is applied to the eigenvalue problem $HM x = lambda x$ with symmetric positive definite H and M. It is shown that each eigenvalue $lambda$ is computed with high relative accuracy and that the relative error $|deltalambda|/lambda$ of the computed approximation $lambda+deltalambda$ is, up to a factor of the dimension, of order boldmath${varepsilon}$unboldmath${min_{Deltain{cal D}}kappa_2(Delta HDelta) + min_{Deltain{cal D}}kappa_2(Delta MDelta)}$. The new algorithm can also be used for accurate SVD computation of a single matrix G that admits an accurate factorization $G=B^{tau}C$." @default.
• W2030717234 created "2016-06-24" @default.
• W2030717234 creator A5068311458 @default.
• W2030717234 date "1998-10-01" @default.
• W2030717234 modified "2023-09-24" @default.
• W2030717234 title "Accurate Computation of the Product-Induced Singular Value Decomposition with Applications" @default.
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• W2030717234 doi "https://doi.org/10.1137/s0036142995292633" @default.
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