Polynomial preconditions for the CG method on the CM2
Préconditionnement polynomial pour la méthode du gradient conjugué sur CM-2
Abstract
This paper is concerned with the implementation of parallel iterative methods for solving large sparse symmetric positive definite linear systems arising form finite difference methods, Ax=b, on an SIMD computer, the CM-2. Specifically, we are interested in the Conjugate Gradient (CG) method introduced by Hestenes and Stiefel. This method is a popular method and effective linear systems solver, notably when combine with a preconditioner, one attractive possibility considered by Ashby or Ciarlet, Meurant, Perlot or Freud or Johnson, Mitchell and Paul is polynomial preconditioning. Its main advantage is its suitability for vector and/or parallel computers, when the matrix by vector product is parallelizable. Whenever A has a regular sparsity structure (multidiagonal), polynomial preconditioning is effective on parallel machine.
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