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Book Synopsis
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.

Core-Chasing Algorithms for the Eigenvalue

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    A Paperback / softback by Jared L. Aurentz, Thomas Mach, Leonardo Robol

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      Publisher: Society for Industrial & Applied Mathematics,U.S.
      Publication Date: Publication Date: 30/07/2018
      ISBN13: 9781611975338, 978-1611975338
      ISBN10: 1611975336
      Also in:
      Algorithms and data structures Applied mathematics

      Description

      Book Synopsis
      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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