Computing eigenspaces with specified eigenvalues of a regular matrix pair \((A,B)\) and condition estimation: Theory, algorithms and software
type: Item
instance of: scholarly article
title: Computing eigenspaces with specified eigenvalues of a regular matrix pair \((A,B)\) and condition estimation: Theory, algorithms and software
zbMATH Open document ID: 0859.65036
DOI: 10.1007/BF02142813
author: Bo Kågström
author: Peter Poromaa
published in: Numerical Algorithms
publication date: 1997-03-25T00:00:00Z
review text: A regular matrix pair \((A,B)\) and \((A-\lambda B)\) matrix pencils are considered. A pair of deflating subspaces with specified eigenvalues, error bounds of the eigenvalues and eigenspaces, condition estimation are computed using LAPACK software. The direct orthogonal transformation method for reordering eigenvalues in the generalized Schur form is overviewed. Direct reordering algorithms with generalized backward stability are discussed. The solution of a generalized Sylvester equation is involved. Theory and algorithms for computing condition numbers and error bounds for eigenvalues and deflating subspaces of a regular matrix are collected. A FORTRAN 77 software for computing deflating subspaces with specified eigenvalues, condition numbers and error bounds is developed and described. Computational experiments that illustrate the accuracy and reliability of the software are carried out.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 946977
zbMATH Keywords: complexity
zbMATH Keywords: numerical examples
zbMATH Keywords: matrix pair
zbMATH Keywords: matrix pencils
zbMATH Keywords: deflating subspaces
zbMATH Keywords: eigenvalues
zbMATH Keywords: error bounds
zbMATH Keywords: eigenspaces
zbMATH Keywords: generalized Schur form
zbMATH Keywords: reordering algorithms
zbMATH Keywords: backward stability
zbMATH Keywords: Sylvester equation
zbMATH Keywords: condition numbers
describes a project that uses: CONEST
describes a project that uses: LAPACK
describes a project that uses: CLAPACK
describes a project that uses: SONEST
describes a project that uses: DSUBSP
describes a project that uses: Algorithm 674
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 946977