Volume 3, pp. 24-38, 1995.

Parallel, synchronous and asynchronous two-stage multisplitting methods

Rafael Bru, Violeta Migallón, José Penadés, and Daniel B. Szyld


Different types of synchronous and asynchronous two-stage multisplitting algorithms for the solution of linear systems are analyzed. The different algorithms which appeared in the literature are reviewed, and new ones are presented. Convergence properties of these algorithms are studied when the matrix in question is either monotone or an $H$-matrix. Relaxed versions of these algorithms are also studied. Computational experiments on a shared memory multiprocessor vector computer are presented.

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Key words

asynchronous methods, two-stage iterative methods, linear systems, multisplittings, parallel algorithms.

AMS subject classifications

65F10, 65F15.

Links to the cited ETNA articles

[3]Vol. 2 (1994), pp. 183-193 Rafael Bru, L. Elsner, and M. Neumann: Convergence of infinite products of matrices and inner-outer iteration schemes

ETNA articles which cite this article

Vol. 4 (1996), pp. 1-13 Robert Fuster, Violeta Migallón, and José Penadés: Non-stationary parallel multisplitting AOR methods
Vol. 5 (1997), pp. 48-61 Andreas Frommer, Hartmut Schwandt, and Daniel B. Szyld: Asynchronous weighted additive Schwarz methods
Vol. 12 (2001), pp. 88-112 M. Jesús Castel, Violeta Migallón, and José Penadés: On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning

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