On the quadratic convergence of Kogbetliantz's algorithm for computing the singular value decomposition

DOI10.1016/0024-3795(86)90173-4zbMath0621.65031OpenAlexW2085126859MaRDI QIDQ1090069

Paul Van Dooren, Christopher C. Paige

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)90173-4

zbMATH Keywords

singular value decompositionquadratic convergenceKogbetliantz's algorithmcyclic Jacobi method

Mathematics Subject Classification ID

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

Related Items (17)

On Kogbetliantz's SVD algorithm in the presence of clusters ⋮ Note on the quadratic convergence of Kogbetliantz's algorithm for computing the singular value decomposition ⋮ An overview of parallel algorithms for the singular value and symmetric eigenvalue problems ⋮ Accuracy of the Kogbetliantz method for scaled diagonally dominant triangular matrices ⋮ Some complexity results in parallel matrix-based signal processing ⋮ On high relative accuracy of the Kogbetliantz method ⋮ On normal and structured matrices under unitary structure-preserving transformations ⋮ Updating the singular value decomposition ⋮ On sharp quadratic convergence bounds for the serial Jacobi methods ⋮ A contribution to the theory and practice of the block Kogbetliantz method for computing the SVD ⋮ A Jacobi-type method for computing balanced realizations ⋮ Accuracy of two SVD algorithms for \(2\times 2\) triangular matrices ⋮ On quadratic convergence bounds for the \(J\)-symmetric Jacobi method ⋮ On efficient implementations of Kogbetliantz's algorithm for computing the singular value decomposition ⋮ Asymptotic Quadratic Convergence of the Two-Sided Serial and Parallel Block-Jacobi SVD Algorithm ⋮ A Jacobi-like algorithm for computing the generalized Schur form of a regular pencil ⋮ Linear convergence of the row cyclic Jacobi and Kogbetliantz methods

Cites Work

• Zur Konvergenz des Jacobi-Verfahrens
• Note on the quadratic convergence of the cyclic Jacobi process
• Almost diagonal matrices with multiple or close eigenvalues
• On the convergence of the classical Jacobi method for real symmetric matrices with non-distinct eigenvalues
• On the quadratic convergence of the special cyclic Jacobi method
• Solution of linear equations by diagonalization of coefficients matrix
• The Cyclic Jacobi Method for Computing the Principal Values of a Complex Matrix
• On the Speed of Convergence of Cyclic and Quasicyclic Jacobi Methods for Computing Eigenvalues of Hermitian Matrices
• Computing the Singular Value Decomposition of a Product of Two Matrices
• Computing the Generalized Singular Value Decomposition
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
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