Accurate computation of singular values in terms of shifted integrable schemes

DOI10.1007/BF03167593zbMath1117.65055MaRDI QIDQ862095

Masashi Iwasaki, Yoshimasa Nakamura

Publication date: 5 February 2007

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical examplesvariable step-sizediscrete Lotka-Volterra systemshift of origin

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Dynamical systems in numerical analysis (37N30) Lattice dynamics; integrable lattice equations (37K60)

Related Items (10)

Discrete Lotka-Volterra with shift algorithm for computing matrix eigenvalues and singular values ⋮ A Bäcklund transformation between two integrable discrete hungry systems ⋮ Integrable discrete hungry systems and their related matrix eigenvalues ⋮ Equality conditions for lower bounds on the smallest singular value of a bidiagonal matrix ⋮ A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix ⋮ The ultradiscrete Toda lattice and the Smith normal form of bidiagonal matrices ⋮ Error analysis of the mdLVs algorithm for computing bidiagonal singular values ⋮ A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system ⋮ Conserved quantities of the integrable discrete hungry systems ⋮ An application of the Kato-Temple inequality on matrix eigenvalues to the dqds algorithm for singular values

Uses Software

• ATLAS
• LAPACK

Cites Work

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• A Gershgorin-type lower bound for the smallest singular value
• Accurate singular values and differential qd algorithms
• Singular value decomposition and least squares solutions
• The discrete Lotka-Volterra system computes singular values
• Accurate Singular Values of Bidiagonal Matrices
• LAPACK Users' Guide
• Discrete-time Volterra chain and classical orthogonal polynomials
• Conserved Quantities of “Random-Time Toda Equation”
• On the convergence of a solution of the discrete Lotka Volterra system
• An application of the discrete Lotka–Volterra system with variable step-size to singular value computation

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