An efficient conjugate gradient preconditioner for Toeplitz systems. (English) Zbl 0691.65016
The authors consider the conjugate gradient method for the solution of a system of linear equations with a possibly perturbed positive definite Toeplitz matrix T. They suggest a preconditioning matrix which arises naturally from the triangular decomposition of a characteristic submatrix of T. Some analysis of the presented method is given and its performance is tested numerically. The method is a variant of incomplete factorization methods.
Reviewer: Z.Dostal
MSC:
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
conjugate gradient method; Toeplitz matrix; preconditioning matrix; triangular decomposition; incomplete factorization methodsReferences:
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