Sparse approximate inverse preconditioners based on a revised Cholesky factorization

Sparse approximate inverse(SAI)preconditioner based on a revised Cholesky factorization is presented in this paper. The traditional Cholesky factorization is firstly revised to cope with the matrix arising from electric field integral equations, which is a complex symmetric matrix, then this revised Cholesky factorization is applied to construct SAI preconditioner for the multilevel fast multipole algorithm(MLFMA). Numerical experiments show that SAI preconditioner constructed by the revised Cholesky factorization performs more efficiently than the previous SAI constructed from QR factorization.