Shift for nonsymmetric generalised eigenvalue problems


Berns-Muller, J. and Spence, A., 2006. Shift for nonsymmetric generalised eigenvalue problems. SIAM Journal On Matrix Analysis and Applications (SIMAX), 28 (4), pp. 1069-1082.

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    In this paper we analyze inexact inverse iteration for the nonsymmetric generalized eigenvalue problem Ax = λMx, where M is symmetric positive definite and the problem is diagonalizable. Our analysis is designed to apply to the case when A and M are large and sparse and preconditioned iterative methods are used to solve shifted linear systems with coefficient matrix A − σM. We prove a convergence result for the variable shift case (for example, where the shift is the Rayleigh quotient) which extends current results for the case of a fixed shift. Additionally, we consider the approach from [V. Simoncini and L. Elden, BIT, 42 (2002), pp. 159–182] to modify the right-hand side when using preconditioned solves. Several numerical experiments are presented thatillustrate the theory and provide a basis for the discussion of practical issues.


    Item Type Articles
    CreatorsBerns-Muller, J.and Spence, A.
    Uncontrolled Keywordseigenvalue approximation, inverse iteration, iterative methods
    DepartmentsFaculty of Science > Mathematical Sciences
    ID Code173
    Additional InformationThis is the author's final, peer-reviewed version. ©Society for Industrial and Applied Mathematics


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