摘要
We discuss the convergence property of the Lanczos method for solving a complex shifted Hermitian linear system （αI ＋ H）x = f. By showing the colinear coefficient of two system＇s residuals, our convergence analysis reveals that under the condition Re（α） ＋ λmin（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.
We discuss the convergence property of the Lanczos method for solving a complex shifted Hermitian linear system （αI ＋ H）x = f. By showing the colinear coefficient of two system＇s residuals, our convergence analysis reveals that under the condition Re（α） ＋ λmin（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.
