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portada Core-Chasing Algorithms for the Eigenvalue Problem
Type
Physical Book
Publisher
Author
Collection
Fundamentals of Algorithms
Year
2018
Language
English
Pages
148
Format
Paperback
Dimensions
22.9x15.2 cm
ISBN13
9781611975338

Core-Chasing Algorithms for the Eigenvalue Problem

Jared L. Aurentz;Thomas Mach;Leonardo Robol;Raf Vandebril;David S. Watkins (Author) · SIAM - Society for Industrial and Applied Mathematics · Paperback

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

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Synopsis "Core-Chasing Algorithms for the Eigenvalue Problem"

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.

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.

This book will be of interest to researchers in numerical linear algebra and their students.

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