On using the shifted minimal residual method for quantum-mechanical wave packet simulation

抄録

We apply the shifted minimum residual method to a shifted linear system $(A+i\sigma I){\bf x}={\bf b}$ arising from quantum-mechanical wave packet simulation and discuss its advantages and disadvantages, comparing it with the widely used COCG method. Although the method requires more vector operations per iteration than the COCG method, it enjoys such nice properties as being free from breakdown, monotonic decrease of the residual norm and applicability to Hermitian-plus-shift systems, and can be a method of choice in some cases. Application of the method to the case of multiple shifts is also discussed.