Acceleration of inverse subspace iteration with Newton's method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:259

Article; Proceedings Paper

El Khoury, G.¹  Nechepurenko, Yu. M.²  Sadkane, M.¹ 

[1] Univ Brest, CNRS, CS 93837, Lab Math Bretagne Atlant,UMR 6205, F-29285 Brest 3, France

[2] Russian Acad Sci, Inst Numer Math, Moscow 119333, Russia

关键词: Inverse subspace iteration;    Newton's method;    Eigenvalue;    Invariant subspace;    Sylvester equation;    Preconditioning;   

DOI  :  10.1016/j.cam.2013.06.046

来源: Elsevier

【 摘 要 】

This work is focused on the computation of the invariant subspace associated with a separated group of eigenvalues near a specified shift of a large sparse matrix. First, we consider the inverse subspace iteration with the preconditioned GMRES method. It guarantees a convergence to the desired invariant subspace but the rate of convergence is at best linear. We propose to use it as a preprocessing for a Newton scheme which necessitates, at each iteration, the solution of a Sylvester type equation for which an iterative algorithm based on the preconditioned GMRES method is specially devised. This combination results in a fast and reliable method. We discuss the implementation aspects and propose a theory of convergence. Numerical tests are given to illustrate our approach. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free