A differential equation approach to the singular value decomposition of bidiagonal matrices

DOI10.1016/0024-3795(86)90278-8zbMath0601.15005OpenAlexW2036229744WikidataQ115364358 ScholiaQ115364358MaRDI QIDQ1080916

Moody T. Chu

Publication date: 1986

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(86)90278-8

zbMATH Keywords

asymptotic behaviorsingular value decompositionToda latticebidiagonal matricesQR algorithmcontinuous approximationautonomous ordinary differential systemGolub-Kahan SVD algorithm

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21)

Related Items

The SVD flows on generic symplectic leaves are completely integrable, Matrix differential equations: a continuous realization process for linear algebra problems, Linearizing Toda and SVD flows on large phase spaces of matrices with real spectrum, Tensor approximation approach to calculation of singular values and vectors for SVD problem, Poisson geometry of the analog of the Miura maps and Bäcklund-Darboux transformations for equations of Toda type and periodic Toda flows, Isospectral deformations of random Jacobi operators, Accurate similarity transformation derived from the discrete Lotka-Volterra system for bidiagonal singular values, Self-equivalent flows associated with the generalized eigenvalue problem, Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson–Lie groups

Uses Software

• LINPACK

Cites Work

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• Singular value decomposition and least squares solutions
• Ordinary Differential Equations and the Symmetric Eigenvalue Problem
• Asymptotic analysis of Toda lattice on diagonalizable matrices
• The Generalized Toda Flow, the QR Algorithm and the Center Manifold Theory
• On the Global Convergence of the Toda Lattice for Real Normal Matrices and Its Applications to the Eigenvalue Problem
• Calculating the Singular Values and Pseudo-Inverse of a Matrix