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A two-parameter description of any computer is given that characterizes the performance of serial, pipelined, and array-like architectures. The first parameter (r∞) is the traditional maximum performance in megaflops, and the new second parameter (n½) measures the apparent parallelism of the computer. For computers with a single instruction stream (unicomputers), the relative performance of two algorithms on the same computer depends only on n½ and the average vector length of the algorithm. The performance of a family of FACR direct methods for solving Poisson's equation is optimized on the basis of this characterization.