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

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