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

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

Published online: 2013-06

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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.

• Keywords

Hermitian matrix Complex shifted linear system Lanczos method

65F10 65Y20.

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@Article{JCM-31-326, author = {}, title = {On Convergence Property of the Lanczos Method for Solving a Complex Shifted Hermitian Linear System}, journal = {Journal of Computational Mathematics}, year = {2013}, volume = {31}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1212-m4186}, url = {http://global-sci.org/intro/article_detail/jcm/9737.html} }
TY - JOUR T1 - On Convergence Property of the Lanczos Method for Solving a Complex Shifted Hermitian Linear System 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 KW - Complex shifted linear system KW - Lanczos method AB -

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.

Guiding Gu. (2019). On Convergence Property of the Lanczos Method for Solving a Complex Shifted Hermitian Linear System. Journal of Computational Mathematics. 31 (3). 326-334. doi:10.4208/jcm.1212-m4186
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