## Parallel, synchronous and asynchronous two-stage multisplitting methods

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

### Abstract

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.

Full Text (PDF) [237 KB]

### Key words

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

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