Monotonic sequences and rates of convergence of asynchronized iterative methods (Q1210402)

The authors study the effect of varying the number of processors on the rate of convergence of the asynchronized parallel block Jacobi method associated with monotone matrices. Under certain assumptions, increasing the number of processors in relation to the number of blocks slows down the convergence. One reason is that increasing the number of processors implies that local approximations are computed from a much earlier global approximation from the host node. The present study of the problem does not assume a fixed iteration matrix.