A modified iterative refinement algorithm for efficient solution of parameter-dependent sets of linear equations

A modified iterative refinement (MIR) algorithm is presented that reduces the time required to solve systems of linear equations that arise when using the method of moments to analyze electromagnetic problems over a band of frequencies. In such an analysis one typically factors the system matrix and solves the linear system at each analysis frequency. With MIR, the LU factorization of the system matrix obtained at one frequency is used to compute solutions at several additional nearby frequencies, often resulting in a major savings in computational effort. Since MIR is not an interpolation technique, answers obtained are numerically exact to any desired degree of precision.