Parallel preconditioners for the conjugate gradient algorithm using Gram–Schmidt and least squares methods

Abstract

This paper is devoted to the study of some preconditioned conjugate gradient algorithms on parallel computers. The considered preconditioners (presented in [J. Straubhaar, Preconditioners for the conjugate gradient algorithm using Gram–Schmidt and least squares methods, Int. J. Comput. Math. 84 (1) (2007) 89–108]) are based on incomplete Gram–Schmidt orthogonalization and least squares methods. The construction of the preconditioner and the resolution are treated separately. Numerical tests are performed and speed-up curves are presented in order to evaluate the performance of the algorithms.