Core-Chasing Algorithms for the Eigenvalue Problem

Core-Chasing Algorithms for the Eigenvalue Problem
PDF
  • eBook:
    Core-Chasing Algorithms for the Eigenvalue Problem
  • Author:
    Jared L. Aurentz, Thomas Mach, Leonardo Robol, Raf Vandebril
  • Edition:
    -
  • Categories:
  • Data:
    July 10, 2018
  • ISBN:
    1611975336
  • ISBN-13:
    9781611975338
  • Language:
    English
  • Pages:
    155 pages
  • Format:
    PDF

Book Description
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.

Content

1. Core Transformations
2. Francis’s Algorithm
3. Francis’s Algorithm as a Core-Chasing Algorithm
4. Some Special Structures
5. Generalized and Matrix Polynomial Eigenvalue Problems
6. Beyond Upper Hessenberg Form

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