Year: 2013
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 326–334
Abstract
We discuss the convergence property of the Lanczos method for solving a complex shifted Hermitian linear system $(α I + H)x = f$. By showing the colinear coefficient of two system's residuals, our convergence analysis reveals that under the condition $Re(α)+ λ _{min}(H)>0$, the method converges faster than that for the real shifted Hermitian linear system $(Re(α) I+H)x=f$. Numerical experiments verify such convergence property.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1212-m4186
Journal of Computational Mathematics, Vol. 31 (2013), Iss. 3 : pp. 326–334
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Hermitian matrix Complex shifted linear system Lanczos method.