Linear convergence of the row cyclic Jacobi and Kogbetliantz methods
type: Item
instance of: scholarly article
title: Linear convergence of the row cyclic Jacobi and Kogbetliantz methods
zbMATH Open document ID: 0682.65018
DOI: 10.1007/BF01395779
author: K. Vince Fernando
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133385
review text: The Kogbetliantz method (KM) [cf. \textit{E. Kogbetliantz}, Quart. Appl. Math. 13, 123-132 (1955; Zbl 0066.101)] for computing the singular value decomposition of a matrix is studied. It is indicated how to achieve global convergence of KM by restricting the rotations to certain domains. For triangular matrices, this requires certain constraints concerning the angles of rotations. It is also indicated how this problem can be removed by using a modified cyclic method which was originally proposed by W. M. Gentleman. The author has also extended this analysis to square matrices and proposed a scheme which guarantees global convergence without under- rotations.
reviewed by: J.Hřebíček
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 4117743
zbMATH Keywords: linear convergence
zbMATH Keywords: row cyclic Jacobi method
zbMATH Keywords: Kogbetliantz method
zbMATH Keywords: singular value decomposition
zbMATH Keywords: global convergence
MaRDI profile type: Publication
cites work: Note on the quadratic convergence of Kogbetliantz's algorithm for computing the singular value decomposition
cites work: Q3730938
cites work: An Improved Algorithm for Computing the Singular Value Decomposition
cites work: On Kogbetliantz's SVD algorithm in the presence of clusters
cites work: Q3819898
cites work: The Cyclic Jacobi Method for Computing the Principal Values of a Complex Matrix
cites work: On Jacobi Methods for Singular Value Decompositions
cites work: Q3729914
cites work: Computing the Singular Value Decomposition of a Product of Two Matrices
cites work: On the Speed of Convergence of Cyclic and Quasicyclic Jacobi Methods for Computing Eigenvalues of Hermitian Matrices
cites work: An estimate for the norms of certain cyclic Jacobi operators
cites work: Solution of linear equations by diagonalization of coefficients matrix
cites work: A triangular processor array for computing singular values
cites work: Computing the Generalized Singular Value Decomposition
cites work: On the quadratic convergence of Kogbetliantz's algorithm for computing the singular value decomposition
cites work: Zur Konvergenz des Jacobi-Verfahrens
cites work: Zur quadratischen Konvergenz des Jacobi-Verfahrens.(On quadrative convergence of the Jacobi method)
cites work: On the convergence of the classical Jacobi method for real symmetric matrices with non-distinct eigenvalues
cites work: On the quadratic convergence of the special cyclic Jacobi method
cites work: Note on the quadratic convergence of the cyclic Jacobi process
cites work: Almost diagonal matrices with multiple or close eigenvalues
description: scientific article; zbMATH DE number 4117743