Another Look at Iterative Methods for Elliptic Difference Equations

Iterative methods for solving elliptic difference equations have received new attention because of the recent advent of novel computer architectures and a growing interest in three-dimensional problems. The fundamental characteristic of an iterative method is its rate of convergence. We present here, in the context of the model probelm in two and three dimensions, a very simple theory for determining the rates of convergence of block iterative schemes. This theory is easily extended to general domains, general elliptic problems, and higher dimenstions.

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