Volume 12, pp. 88-112, 2001.

On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning

M. Jesús Castel, Violeta Migallón, and José Penadés


Parallel two-stage iterative methods for the solution of linear systems are analyzed. Convergence properties of both block and multisplitting two-stage methods are investigated either when the number of inner iterations becomes sufficiently large or when the matrix of the linear system is Hermitian positive definite. Comparison theorems for the parallel two-stage methods, based on the number of inner iterations performed, are given. Computational results of these methods on two parallel computing systems are included to illustrate the theoretical results. Also, the use of these methods as preconditioners is studied from the experimental point of view.

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Key words

linear systems, two-stage methods, block methods, multisplitting methods, Hermitian matrix, positive definite matrix, preconditioners, parallel algorithms, monotonicity, distributed memory.

AMS subject classifications

65F10, 65F15.

Links to the cited ETNA articles

[8]Vol. 3 (1995), pp. 24-38 Rafael Bru, Violeta Migallón, José Penadés, and Daniel B. Szyld: Parallel, synchronous and asynchronous two-stage multisplitting methods
[18]Vol. 4 (1996), pp. 1-13 Robert Fuster, Violeta Migallón, and José Penadés: Non-stationary parallel multisplitting AOR methods

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