Core-Chasing Algorithms for the Eigenvalue Problem

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