Bidiagonalization and diagonalization
type: Item
instance of: scholarly article
title: Bidiagonalization and diagonalization
zbMATH Open document ID: 0633.65038
DOI: 10.1016/0898-1221(87)90051-4
publication date: 1987-01-01T00:00:00Z
review text: The author discusses four related topics. In the first it is shown how an \(n\times n\) complex matrix A can be diagonalized, if the diagonalization for a matrix near A is known. The second introduces a modified shift strategy for use with the QR algorithm. The third concerns the fast Givens procedure and the QR algorithm. The last considers the problem of expressing an \(m\times n\) complex A as \(QBP^*\) where P, Q are unitary and B is upper bidiagonal.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F25
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 4030835
zbMATH Keywords: bidiagonalization
zbMATH Keywords: fast Givens transformation
zbMATH Keywords: shift strategy
zbMATH Keywords: QR algorithm
author: William Hager
describes a project that uses: NAPACK
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90051-4
OpenAlex ID: W2000918303
cites work: Least Squares Computations by Givens Transformations Without Square Roots
cites work: Calculating the Singular Values and Pseudo-Inverse of a Matrix
cites work: Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
cites work: Q5185900
cites work: An Improved Algorithm for Computing the Singular Value Decomposition
cites work: The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
cites work: Q3994560
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
cites work: A Stable, Rational QR Algorithm for the Computation of the Eigenvalues of an Hermitian, Tridiagonal Matrix
cites work: Q5674306
published in: Computers & Mathematics with Applications
Recommended article: Q4503828
Recommended article: Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
Recommended article: Bidiagonalization of \((k, k + 1)\)-tridiagonal matrices
Recommended article: Q4430899
Recommended article: Diagonalisation schemes and applications
Recommended article: Bidiagonalization of oscillatory matrices∗
Recommended article: Q4918397
Recommended article: Bidiagonal Factorizations of Totally Nonnegative Matrices
Recommended article: Diagonalization in double frames
Recommended article: Q3437496
description: scientific article; zbMATH DE number 4030835