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The Theory of Matrices in Numerical Analysis

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This book represents an effort to select and present certain aspects of the theory of matrices that are most useful in developing and appraising computational methods for solving systems of linear equations (including the inversion of matrices) and for finding characteristic roots. The solution of linear inequalities and the problems of linear programing are not explicitly considered since there are special difficulties inherent in these problems that are largely combinatorial in character and require a quite different approach.

The list of titles at the end of the book should provide convincing evidence that the problems that are treated here are of considerable interest to numerical analysts, and also to mathematicians. This list is culled from perhaps twice as many titles contained in the author's files: these files are certainly not complete, and the number of publications grows at an accelerating rate. The reason is clear. A finite digital computer can be applied to the solution of functional equations and infinite systems only when finite approximations have been made; and usually the first step toward solving a nonlinear system is to linearize. Thus finite linear systems stand at the heart of all mathematical computation. Moreover as science and technology develop, and computers become more powerful, systems to be handled become larger and require techniques that are more refined and efficient.
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