Core Chasing Algorithms for the Eigenvalue Problem

Jared L. Aurentz, Thomas Mach, Leonardo Robol, Raf Vandebril, David S. Watkins

Research output: Book/ReportBook

Abstract

Eigenvalue computations are ubiquitous in science and engineering. John Francis’s implicitly shifted QR algorithm has been the method of choice for small to medium sized eigenvalue problems since its invention in 1959. This book presents a new view of this classical algorithm. While Francis’s original procedure chases bulges, the new version chases core transformations, which allows the development of fast algorithms for eigenvalue problems with a variety of special structures. This also leads to a fast and backward stable algorithm for computing the roots of a polynomial by solving the companion matrix eigenvalue problem. The authors received a SIAM Outstanding Paper prize for this work.
Original languageEnglish
PublisherSociety of Industrial and Applied Mathematics
Number of pages149
ISBN (Electronic)978-1-61197-534-5
ISBN (Print)978-1-611975-33-8
Publication statusPublished - Jul 2018

Publication series

NameFundamentals of Algorithms

Fingerprint

Eigenvalue Problem
Eigenvalue Computation
Root of a polynomial
QR Algorithm
Companion Matrix
Fast Algorithm
Engineering
Computing

Cite this

Aurentz, J. L., Mach, T., Robol, L., Vandebril, R., & Watkins, D. S. (2018). Core Chasing Algorithms for the Eigenvalue Problem. (Fundamentals of Algorithms). Society of Industrial and Applied Mathematics.

Core Chasing Algorithms for the Eigenvalue Problem. / Aurentz, Jared L.; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S.

Society of Industrial and Applied Mathematics, 2018. 149 p. (Fundamentals of Algorithms).

Research output: Book/ReportBook

Aurentz, JL, Mach, T, Robol, L, Vandebril, R & Watkins, DS 2018, Core Chasing Algorithms for the Eigenvalue Problem. Fundamentals of Algorithms, Society of Industrial and Applied Mathematics.
Aurentz JL, Mach T, Robol L, Vandebril R, Watkins DS. Core Chasing Algorithms for the Eigenvalue Problem. Society of Industrial and Applied Mathematics, 2018. 149 p. (Fundamentals of Algorithms).
Aurentz, Jared L. ; Mach, Thomas ; Robol, Leonardo ; Vandebril, Raf ; Watkins, David S. / Core Chasing Algorithms for the Eigenvalue Problem. Society of Industrial and Applied Mathematics, 2018. 149 p. (Fundamentals of Algorithms).
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