Modified incomplete Cholesky (MIC) methods. (English) Zbl 0767.65017

Gustafsson, Ivar

Preconditioning methods. Analysis and applications, Top. Comput. Math. 1, 265-293 (1991).

[For the entire collection see Zbl 0753.00013.]
Incomplete factorizations as preconditioners for the conjugate gradient method have been applied with great success in order to solve large sparse symmetric linear systems numerically. The author modifies such factorizations by adding to the diagonal those terms that otherwise would be dropped in the incomplete factorization.
This technique is applied to a wide class of problems, including nonsymmetric, derived from elliptic partial differential equations. It is shown that the modified incomplete Cholesky factorizations, when combined with conjugate gradients (MICCG), behave better than several other well known methods.

Reviewer: J.P.Milaszewicz (Buenos Aires)

MSC:

65F10	Iterative numerical methods for linear systems
65F35	Numerical computation of matrix norms, conditioning, scaling
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N06	Finite difference methods for boundary value problems involving PDEs
65F50	Computational methods for sparse matrices
35J25	Boundary value problems for second-order elliptic equations

Keywords:

finite element; finite difference; elliptic problems; nonsymmetric matrices; incomplete factorizations; conjugate gradient method; large sparse symmetric linear systems; modified incomplete Cholesky factorizations