Two fast algorithms for solving diagonal-plus-semiseparable linear systems

Authors:
Ellen Van Camp;Nicola Mastronardi;Marc Van Barel
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Heverlee 3001, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Heverlee 3001, Belgium and Istituto per le Applicazioni del Calcolo "M. Picone", sez. Bari Consiglio Nazionale ...;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, Heverlee 3001, Belgium
Venue:
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Year:
2004

Citing 1
Cited 3

Fast and Stable Algorithms for Banded Plus Semiseparable Systems of Linear Equations

SIAM Journal on Matrix Analysis and Applications

A Levinson-like algorithm for symmetric strongly nonsingular higher order semiseparable plus band matrices

Journal of Computational and Applied Mathematics
A multiple shift QR-step for structured rank matrices

Journal of Computational and Applied Mathematics
A note on the nullity theorem

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we discuss the structure of the factors of a QR- and a URV-factorization of a diagonal-plus -semiseparable matrix. The Q-factor of a QR-factorization has the diagonal-plus-semiseparable structure. The UT- and V-factor of a URV-factorization are semiseparable lower Hessenberg orthogonal matrices. The strictly upper triangular part of the R-factor of a QR- and of a URV-factorization is the strictly upper triangular part of a rank-2 matrix. This latter fact provides a tool to construct a fast QR-solver and a fast URV-solver for linear systems of the form (D + S)x = b.