Volume 31, Issue 3
On Convergence Property of the Lanczos Method for Solving a Complex Shifted Hermitian Linear System

Guiding Gu

10.4208/jcm.1212-m4186

J. Comp. Math., 31 (2013), pp. 326-334.

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  • 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.

  • History

Published online: 2013-06

  • AMS Subject Headings

65F10, 65Y20.

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