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 of the linear system is the product of nonsingular matrices with specific shape: for a fixed matrix and real numbers . Although having the special form, these matrices arise frequently in the discretization of evolutionary Partial Differential Equations. The idea is to express as a linear combination of elementary matrices . Hence the solution of the linear system with matrix is a linear combination of the solutions of linear systems with matrices . These systems are solved simultaneously on different processors.