OVERLAPPING BLOCK METHODS FOR SOLVING TRIDIAGONAL SYSTEMS ON TRANSPUTER ARRAYS

This paper considers a simple extension of the block Jacobi iterative method to an overlapping block structure. It is shown how enlarging a system of algebraic equations by including duplicate copies of several rows, leads to an efficient iterative scheme on a multiprocessor MIMD array. Convergence estimates are provided for a simple model problem. Numerical results are given for the method implemented on transputer arrays in a Meiko computer surface and these are shown to be consistent with the theory.