A Minimal Residual Interpolation Method for Linear Equations with Multiple Right-Hand Sides

Abstract

An efficient method for the solution of systems of linear equations with many right-hand sides is developed. The right-hand sides are assumed to depend smoothly on a parameter. The equations are solved by an iterative method, and a linear least squares approximation is used as initial guess. The work spent on the iterations is bounded independently of the number of right-hand sides. The method is applied to the solution of Maxwell's equations of electromagnetics in the frequency domain. The efficiency of the method is illustrated by computing the monostatic radar cross section around an aircraft model.