Differential qd Algorithm with Shifts for Rank-Structured Matrices

Although QR iterations dominate in eigenvalue computations, there are several important cases when alternative LR-type algorithms may be preferable, in particular, in the symmetric tridiagonal case where the differential qd algorithm with shifts (dqds) proposed by Fernando and Parlett enjoys often f...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:SIAM journal on matrix analysis and applications Jg. 33; H. 4; S. 1153 - 1171
1. Verfasser: Zhlobich, Pavel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Schlagworte:
Accuracy
Algorithms
Eigenvalues
Experiments
Linear algebra
ISSN:0895-4798, 1095-7162
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Although QR iterations dominate in eigenvalue computations, there are several important cases when alternative LR-type algorithms may be preferable, in particular, in the symmetric tridiagonal case where the differential qd algorithm with shifts (dqds) proposed by Fernando and Parlett enjoys often faster convergence while preserving high relative accuracy. In eigenvalue computations for rank-structured matrices, the QR algorithm is also a popular choice since, in the symmetric case, the rank structure is preserved. In the unsymmetric case, however, the QR algorithm destroys the rank structure and, hence, LR-type algorithms come in to play once again. In the current paper we adapt several variants of qd algorithms to quasi-separable matrices. Remarkably, one of them, when applied to Hessenberg matrices, becomes a direct generalization of the dqds algorithm for tridiagonal matrices. Therefore, it can be applied to such important matrices as companion and confederate and provides an alternative algorithm for finding roots of a polynomial represented in a basis of orthogonal polynomials. Results of preliminary numerical experiments are presented. [PUBLICATION ABSTRACT]
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0895-4798
1095-7162
DOI:10.1137/110857155