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An incomplete inverse as a preconditioner for the conjugate gradient method. (English) Zbl 0765.65041
Author’s summary: This paper introduces a new preconditioner with a superconvergence for the conjugate gradient method for solving a system of linear equations in a banded structure. The idea is based upon an innovative method of the author to decompose a symmetric matrix into its inverse, and the preconditioner is the result of an incomplete decomposition, i.e. an approximation to the inverse. By the presented preconditioner, the rate of convergence can be significantly improved. Examples to demonstrate the improvement of the rate of convergence and the speedup implemented on an Alliant/FX8 computer are included.
Reviewer: J.Zítko (Praha)

MSC:
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
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