A program generator for the incomplete cholesky conjugate gradient (ICCG) method with a symmetrizing preprocessor

Abstract

This paper is an extension of our previous paper “A program generator for the Incomplete LU-decomposition-Conjugate Gradient (ILUCG) method” which appeared in Computer Physics Communications. In that paper we presented a generator program which produced a code package to solve the system of equations A x = b b , where A is an arbitrary nonsingular matrix, by the ILUCG method. In the present paper we offer an alternative generator program which produces a code package applicable to the case where A is symmetric and positive definite. The numerical algorithm used is the Incomplete Cholesky Conjugate Gradient (ICCG) method of Meijerink and Van der Vorst which executes approximately twice as fast per iteration as the ILUCG method. In addition, we provide an optional preprocessor to treat the case of a not diagonally dominant nonsymmetric and nonsingular matrix A by solving the equation A T A x = A T b .