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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.
Preconditioners for the conjugate gradient algorithm using Gram-Schmidt and least squares methods
This paper is devoted to the study of some preconditioners for the conjugate gradient algorithm used to solve large sparse linear and symmetric positive definite systems. The construction of a preconditioner based on the Gram-Schmidt orthogonalization process and the least squares method is presented. Some results on the condition number of the preconditioned system are provided. Finally, numerical comparisons are given for different preconditioners.
Preconditioners for the conjugate gradient algorithm using Gram–Schmidt and least squares methods
This paper is devoted to the study of some preconditioners for the conjugate gradient algorithm used to solve large sparse linear and symmetric positive definite systems. The construction of a preconditioner based on the Gram–Schmidt orthogonalization process and the least squares method is presented. Some results on the condition number of the preconditioned system are provided. Finally, numerical comparisons are given for different preconditioners.