Multiple Iterative Solution of Linear Algebraic Systems with a Partially Varying Matrix

An iterative algorithm for solving a series of linear algebraic systems with partially varying coefficient matrix is suggested. Simple formulas for evaluating the speed up obtained are derived and used in choosing the related parameters. As examples, the choice of the drop tolerance and initial guesses are considered. Multiple solutions of linear systems of orders 708, 1416, 3540, 4425 arising in computing (by the method of moments) the electric capacity of two strips on a dielectric layer above a perfect conductive plane in the range of dielectric permeability is analyzed. As compared with Gaussian elimination, a 49 times speed up in solving 1000 linear systems of order 4425 is achieved.