On a modification of the QZ algorithm with fast Givens rotations
type: Item
instance of: scholarly article
title: On a modification of the QZ algorithm with fast Givens rotations
zbMATH Open document ID: 0613.65033
DOI: 10.1007/BF02240099
author: H. P. Märchy
published in: Computing
publication date: 1987-01-01T00:00:00Z
review text: It is explained, how Householder reflections can be replaced by fast Givens rotations in the first and second step of the QZ algorithm. A count of the required operations for the two steps shows, that the modified first step does need less operations, but that the modified second step needs only insigificantly less operations in comparison with the original QZ algorithm. On the base of this fact a modification of the second step is proposed. The resulting new algorithm is called FQZ algorithm, which has the same numerical properties as the QZ algorithm, if a correct scaling is applied.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F25
zbMATH DE Number: 3992792
zbMATH Keywords: generalized unsymmetric algebraic eigenvalue problem
zbMATH Keywords: rounding error
zbMATH Keywords: Householder reflections
zbMATH Keywords: fast Givens rotations
zbMATH Keywords: QZ algorithm
zbMATH Keywords: FQZ algorithm
zbMATH Keywords: scaling
describes a project that uses: IMSL Numerical Libraries
MaRDI profile type: Publication
cites work: Q3339168
cites work: Least Squares Computations by Givens Transformations Without Square Roots
cites work: Q5185900
cites work: Q4404310
cites work: Some Thoughts on the QZ Algorithm for Solving the Generalized Eigenvalue Problem
cites work: An Algorithm for Generalized Matrix Eigenvalue Problems
cites work: Fast givens rotations for orthogonal similarity transformations
cites work: The Combination Shift $QZ$ Algorithm
cites work: Q5674306
full work available at URL: https://doi.org/10.1007/bf02240099
OpenAlex ID: W429641120
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description: scientific article; zbMATH DE number 3992792