On K-Line and K x K Block Iterative Schemes for a Problem Arising in 3-D Elliptic Difference Equations

摘要

Novel computer architectures and a desire to solve three-dimensional problems have together aroused new interest in iterative methods for computing solutions to elliptic difference equations. Block iterative methods are particularly attractive for vector machines, such as the CRAY-1. Plane iterative schemes reduce a three-dimensional elliptic system to two-dimensional systems. We analyze the convergence rate of k-line and k x k block iterative methods for solving these two-dimensional problems. (Author)