The Convergence of the Almost Linear Parallel Iterations
by
Ljiljana Cvetkovic

A non-stationary parallel algorithm (synchronous and asynchronous version) based on the AOR-type methods have been investigated by Arnal et all. They have proved some convergence results for the case when linear part is an M- or an H-matrix. These methods can be very efficient when implemented on distributed memory multiprocessor. Since their efficiency depends on the choice of two relaxation parameters, it seems interesting to find the area of convergence, as wide as possible. A new convergence theorem for strictly diagonally dominant case will be proved and compared to the known one. The generalization to the H-matrix case will be also proved.

Date received: February 20, 2001