### Projections obliques alternées pour les systèmes linéaires couplés

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**Abstract:** The numerical solution of large sparse systems is an active domain of research, mainly, because it is an important key for the numerical solution of

partial differential equations (PDE) which arise from the simulation of physics and engineering problems.

The domain decomposition method is worth studying because it lends itself to parallelization. The linear systems resulting from the discretization of

domain decomposition problems are called coupled systems. In this work we propose the use of alternating oblique projections for the solution of

coupled linear systems. This is a descent method where the descent direction is defined by using alternating oblique projections onto the search

subspaces. The choice of the stepsize is optimal in the norm $\norm{.}_A$. We prove that this method is a preconditioned simple gradient (Uzawa)

method with a particular preconditioner. Finally, we apply this preconditioner to improve the conjugate gradient method.

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**Date:** 2002-11-01