On Convergence Property of MINRES Method for Solving a Complex Shifted Hermitian Linear System

We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.

• Guiding Gu
• Guo Liu

• complex shifted linear system
• Hermitian matrix
• MINRES method.

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