Parallel Newton-Chebyshev Polynomial Preconditioners for the Conjugate Gradient method
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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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