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

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.