TY - JOUR
T1 - On Convergence Property of the Lanczos Method for Solving a Complex Shifted Hermitian Linear System
AU - Guiding Gu
JO - Journal of Computational Mathematics
VL - 3
SP - 326
EP - 334
PY - 2013
DA - 2013/06
SN - 31
DO - http://doi.org/10.4208/jcm.1212-m4186
UR - https://global-sci.org/intro/article_detail/jcm/9737.html
KW - Hermitian matrix, Complex shifted linear system, Lanczos method.
AB - <p style="text-align: justify;">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&#39;s residuals, our convergence analysis reveals that under the condition $Re(α)+ λ _{min}(H)&gt;0$, 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.</p>