In this paper we consider the arithmetic mean preconditioner for the conjugate gradient method. This preconditioner is designed to be implemented on a multiprocessor system that can execute concurrently different tasks on vector processors.Some spectral bounds for the preconditioner have been obtained. A comparison between this preconditioner and the SSOR preconditioner has been carried out on different test-matrices. Also the m-step preconditioners generated by the arithmetic mean preconditioner and by the SSOR preconditioner have been compared.
The arithmetic mean preconditioner for multivector computers / Galligani, Emanuele; V., Ruggiero. - In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. - ISSN 0020-7160. - STAMPA. - 44:(1992), pp. 207-222.