The generalized singular value decomposition and the general (A-\(\lambda\) B)-problem

DOI10.1007/BF01934915zbMath0552.65038OpenAlexW2039333245MaRDI QIDQ801633

Bo Kågström

Publication date: 1984

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01934915

zbMATH Keywords

numerical examplessingular value decompositionKronecker canonical formmatrix pencilrange nullspace separation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items

Computing stable eigendecompositions of matrix pencils, The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms, On worst-case condition numbers of a multiple nonzero finite generalized singular value, Methods and algorithms of solving spectral problems for polynomial and rational matrices, Two harmonic Jacobi-Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair, A cross-product free Jacobi-Davidson type method for computing a partial generalized singular value decomposition of a large matrix pair, A Higher-Order Generalized Singular Value Decomposition for Rank-Deficient Matrices, A note on simple nonzero finite generalized singular values, New iterative methods for generalized singular-value problems, On choices of formulations of computing the generalized singular value decomposition of a large matrix pair, A Jacobi-Davidson type method for the generalized singular value problem, Eigenvalue computation in the 20th century, Numerical methods and questions in the organization of calculus. XII. Transl. from the Russian

Uses Software

• JNF
• Matlab
• EISPACK

Cites Work

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• The computation of Kronecker's canonical form of a singular pencil
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• Towards a Generalized Singular Value Decomposition
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• A General Matrix Eigenvalue Algorithm
• Generalizing the Singular Value Decomposition
• Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form
• The Rotation of Eigenvectors by a Perturbation. III
• An Algorithm for Generalized Matrix Eigenvalue Problems