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.
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⟩