Computing the generalized singular values/vectors of large sparse or structured matrix pairs
type: Item
instance of: scholarly article
title: Computing the generalized singular values/vectors of large sparse or structured matrix pairs
zbMATH Open document ID: 0856.65041
author: Hongyuan Zha
published in: Numerische Mathematik
publication date: 1997-02-24T00:00:00Z
review text: The author derives an algorithm for computing a few extreme generalized singular values and the corresponding vectors of a sparse or structural matrix pair \(\{A,B\}\). The algorithm is based on the CS decomposition and the Lanczos bidiagonalization process. At each iteration step of the Lanczos process, the solution to a linear least squares problem with \((A^T,B^T)^T\) as the coefficient matrix is approximately computed, and this consists in the only interface of the algorithm with the matrix pair \(\{A,B\}\). Some numerical results are also given to demonstrate the feasibility and efficiency of the algorithm.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 932049
zbMATH Keywords: CS decomposition
zbMATH Keywords: algorithm
zbMATH Keywords: generalized singular values
zbMATH Keywords: sparse or structural matrix pair
zbMATH Keywords: Lanczos bidiagonalization
zbMATH Keywords: linear least squares problem
zbMATH Keywords: numerical results
reviewed by: Prem Narain
MaRDI profile type: Publication
full work available at URL: s002110050175
OpenAlex ID: W2000512102
DOI: 10.1007/S002110050175
description: scientific article; zbMATH DE number 932049