On the stability of the incomplete Cholesky decomposition for a singular perturbed problem, where the coefficient matrix is not an M-matrix

Abstract

The incomplete Cholesky decomposition is known as an excellent smoother in a multigrid iteration and as a preconditioner for the conjugate gradient method. However, the existence of the decomposition is only ensured if the system matrix is an M-matrix. It is well-known that finite element methods usually do not lead to M-matrices. In contrast to this restricting fact, numerical experiments show that, even in cases where the system matrix is not an M-matrix the behaviour of the incomplete Cholesky decomposition apparently does not depe Show more