Core-chasing algorithms for the Eigenvalue problem

Core-chasing algorithms for the Eigenvalue problem

by Aurentz, Jared L.

Type Book
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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 …

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Title Statements

  • Full title :Core-chasing algorithms for the Eigenvalue problem / Jared L. Aurentz, Thomas Mach, Leonardo Robol, Raf Vandebril, and David S. Watkins.

Summary

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.

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Edition Statements

  • Publication Date:[2018].

Publication Statements

Notes

In SIAM e-books.

The Physical Object

  • Description:1 ressource en ligne (x, 147 pages).

Edition Identifiers

  • ISBN:9781611975345, 1611975344
  • oclc:on1114148260
  • LC Classification:QA193
  • Dewey Decimal:512.9/436

Table of Contents

Core transformations -- Francis's algorithm -- Francis's algorithm as a core-chasing algorithm -- Some special structures -- Generalized and matrix polynomial Eigenvalue problems -- Beyond Upper Hessenberg Form.

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Subjects

Algebras, Linear Algèbre linéaire Backward stability e-books Eigenvalue computation eigenvalues Francis algorithm Livres numériques matrices QR algorithm QR decomposition Valeurs propres

Writers

Aurentz, Jared L. Mach, Thomas, (Professor of Mathematics) Robol, Leonardo Vandebril, Raf Watkins, David S.

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