We consider techniques for the solution of linear systems and eigenvalue problems. We are concerned with large-scale applications where the matrix will be large and sparse. We discuss both direct and iterative techniques for the solution of sparse equations, contrasting their strengths and weaknesses and emphasizing that combinations of both are necessary in the arsenal of the applications scientist. We briefly review matrix diagonalization techniques for large-scale problems. Keywords: sparse matrices, sparse linear equations, direct methods, iterative methods, large-scale applications, matrix diagonalization, eigenproblems, mathematical software. AMS(MOS) subject classifications: 65F05, 65F50. 1 This paper is based on an invited presentation at the meeting "Supercomputing, Collision Processes and Applications" that was held at The Queen's University of Belfast from 14th to 16th September 1998 to mark the retirement of Professor P G Burke CBE FRS. The Proceedings will be publish...
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