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Overall Objectives
New Software and Platforms
Bilateral Contracts and Grants with Industry
Bibliography
Overall Objectives
New Software and Platforms
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

Fractional decomposition of matrices and parallel computing

In [40] we are interested in the design of parallel numerical schemes for linear systems. We give an effective solution to this problem in the following case: the matrix A of the linear system is the product of p nonsingular matrices Aim with specific shape: Ai=I-hiX for a fixed matrix X and real numbers hi. Although having the special form, these matrices Ai arise frequently in the discretization of evolutionary Partial Differential Equations. The idea is to express A-1 as a linear combination of elementary matrices Ai-k. Hence the solution of the linear system with matrix A is a linear combination of the solutions of linear systems with matrices Aik. These systems are solved simultaneously on different processors.