In:
East Asian Journal on Applied Mathematics, Global Science Press, Vol. 5, No. 2 ( 2015-05), p. 160-175
Abstract:
The shift-and-invert Arnoldi method is a most effective approach to compute a few eigenpairs of a large non-Hermitian Toeplitz matrix pencil, where the Gohberg-Semencul formula can be used to obtain the Toeplitz inverse. However, two large non-Hermitian Toeplitz systems must be solved in the first step of this method, and the cost becomes prohibitive if the desired accuracy for this step is high — especially for some ill-conditioned problems. To overcome this difficulty, we establish a relationship between the errors in solving these systems and the residual of the Toeplitz eigenproblem. We consequently present a practical stopping criterion for their numerical solution, and propose an inexact shift-and-invert Arnoldi algorithm for the generalised Toeplitz eigenproblem. Numerical experiments illustrate our theoretical results and demonstrate the efficiency of the new algorithm.
Type of Medium:
Online Resource
ISSN:
2079-7362
,
2079-7370
DOI:
10.4208/eajam.010914.130415a
Language:
English
Publisher:
Global Science Press
Publication Date:
2015
detail.hit.zdb_id:
2687785-5
