Parallel Newton-Chebyshev Polynomial Preconditioners for the Conjugate Gradient method

Luca Bergamaschi; Angeles Martinez

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arXiv · 2008.01440

Parallel Newton-Chebyshev Polynomial Preconditioners for the Conjugate Gradient method

Luca Bergamaschi·Angeles Martinez

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Abstract

In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix equation X^{-1} = A and the Chebyshev polynomials for preconditioning. We propose a simple modification of one parameter which avoids clustering of extremal eigenvalues in order to speed-up convergence. We provide results on very large matrices (up to 8 billion unknowns) in a parallel environment showing the efficiency of the proposed class of preconditioners.

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Luca Bergamaschi, Angeles Martinez. 2020-08-04. Parallel Newton-Chebyshev Polynomial Preconditioners for the Conjugate Gradient method. https://arxiv.org/abs/2008.01440

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