Robust approximate inverse preconditioning for the conjugate gradient method. (English) Zbl 0985.65035
The authors present a stabilized approximate inverse algorithm for arbitrary symmetric positive definite matrices to be used in preconditioned conjugate gradient methods. They also investigate another approach to prevent breakdowns that is based on the technique of diagonally compensated reduction of positive off-diagonal entries. Numerical results for problems arising from finite element discretizations of elasticity and diffusion problems illustrate the performance of the algorithms.
Reviewer: R.H.W.Hoppe (München)
MSC:
65F35 | Numerical computation of matrix norms, conditioning, scaling |
65F50 | Computational methods for sparse matrices |
65F10 | Iterative numerical methods for linear systems |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35J25 | Boundary value problems for second-order elliptic equations |
65Y20 | Complexity and performance of numerical algorithms |