Pole Expansion for Solving a Type of Parametrized Linear Systems in Electronic Structure Calculations

We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to linear systems for a small set of fixed parameters. Combined with either direct solvers or preconditioned iterative solvers for each linear system with a fixed parameter, the method is particularly suitable for situations when solutions to a large number of distinct parameters or a large number of right hand sides are required. The method is also simple to parallelize. We demonstrate the applicability of the method to the calculation of the response functions in electronic structure theory. We demonstrate the numerical performance of the method using a benzene molecule and a DNA molecule.