Algorithm design for large-scale computations

Success in large-scale scientific compu tations often depends on algorithm design. Even the fastest machine may prove to be inadequate if insufficient attention is paid to the way in which the computation is organized. We have used several problems from computational physics to illustrate the importance of good algorithms, and we offer some very general principles for designing algorithms. Two subthemes are, first, the strong connection between the algorithm and the architecture of the target machine; and second, the impor tance of non-numerical methods in scien tific computations.