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Polynomial preconditions for the CG method on the CM2

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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Contributor : Olivier Perlot Connect in order to contact the contributor
Submitted on : Tuesday, March 29, 2022 - 4:23:56 PM
Last modification on : Saturday, April 9, 2022 - 3:39:04 AM


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  • HAL Id : hal-03614976, version 1


Pascal Joly, Olivier Perlot. Polynomial preconditions for the CG method on the CM2. Tercera Escuela de Verano en Geometría Diferencial, Ecuaciones Diferenciales Parciales y Análisis Numérico, ACADEMIA COLOMBIANA DE CIENCIAS EXACTAS, FISICAS Y NATURALES, Jun 1996, Bogota, Colombia. ⟨hal-03614976⟩



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