Practical use of polynomial preconditionings for the conjugate gradient method. (English) Zbl 0601.65019
Author’s summary: This paper presents some practical ways of using polynomial preconditionings for solving large sparse linear systems of equations issued from discretizations of partial differential equations. For a symmetric positive definite matrix A these techniques are based on least squares polynomials on the interval [0,b] where b is the Gershgorin estimate of the largest eigenvalue. Therefore, as opposed to previous work in the field, there is no need for computing eigenvalues of A. We formulate a version of the conjugate gradient algorithm that is more suitable for parallel architectures and discuss the advantages of polynomial preconditioning in the context of these architectures.
Reviewer: I.H.Mufti
MSC:
65F10 | Iterative numerical methods for linear systems |
65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
65F50 | Computational methods for sparse matrices |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |