Exponential splittings of products of matrices and accurately computing singular values of long products

DOI10.1016/S0024-3795(99)00273-6zbMath0955.65028MaRDI QIDQ1976915

Suely Oliveira, David E. Stewart

Publication date: 14 February 2001

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

zbMATH Keywords

stabilitynumerical examplesLyapunov exponentsproducts of matricessingular valuesexponential splitting

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (6)

Perturbation theory for approximation of Lyapunov exponents by QR methods ⋮ The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects ⋮ A Jacobi-Davidson type method for the product eigenvalue problem ⋮ The periodic QR algorithm is a disguised QR algorithm ⋮ SVD algorithms to approximate spectra of dynamical systems ⋮ On the error in computing Lyapunov exponents by QR methods

Uses Software

• mctoolbox

Cites Work

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• Perturbation bounds for the \(LDL^ H\) and LU decompositions
• An accurate product SVD algorithm
• Componentwise perturbation bounds for some matrix decompositions
• A spectral theory for linear differential systems
• Relative perturbation results for eigenvalues and eigenvectors of diagonalisable matrices
• Local Lyapunov exponents computed from observed data
• A new algorithm for the SVD of a long product of matrices and the stability of products
• On graded QR decompositions of products of matrices
• On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems
• Matrix Analysis
• Accurate Computation of the Product-Induced Singular Value Decomposition with Applications
• Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds
• Relative Perturbation Techniques for Singular Value Problems

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