Implementation of Jacobi Rotations for Accurate Singular Value Computation in Floating Point Arithmetic

DOI10.1137/S1064827594265095zbMath0894.65016OpenAlexW1970815336MaRDI QIDQ4376215

Zlatko Drmač

Publication date: 10 February 1998

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s1064827594265095

zbMATH Keywords

singular value decompositionerror analysisJacobi methodspectral condition numberfloating point arithmeticrelative accuracymodified Jacobi rotation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Roundoff error (65G50)

Related Items

A Kogbetliantz-type algorithm for the hyperbolic SVD, Batched Computation of the Singular Value Decompositions of Order Two by the AVX-512 Vectorization, Accuracy of the Kogbetliantz method for scaled diagonally dominant triangular matrices, Vectorization of a Thread-Parallel Jacobi Singular Value Decomposition Method, Approximate eigenvectors as preconditioner, Accelerating the SVD block-Jacobi method, On the global convergence of the block Jacobi method for the positive definite generalized eigenvalue problem, Accuracy of two SVD algorithms for \(2\times 2\) triangular matrices, Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices, Implicit standard Jacobi gives high relative accuracy, Quadratic convergence of a special quasi-cyclic Jacobi method

Uses Software

• LAPACK