Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
A proposed numerical accuracy control system
Symposium on Interactive Systems for Experimental Applied Mathematics: Proceedings of the Association for Computing Machinery Inc. Symposium
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Many problems encountered in computing involve the solution of the simultaneous linear equations (1) A x = b where A is a n-by-n matrix, [EQUATION] and b and x are vectors. Most people interested in computing are familiar with the basic concepts involved in solving such a system, but there are several useful refinements and extensions that are not so well known. It is the purpose of this article to introduce the non-expert to these ideas. Several of the newer ideas, as well as clarifications of older ones, are due to J. H. Wilkinson and are summarized in his book. Many people, including this writer, are indebted to G. E. Forsythe for their knowledge of this field. Forsythe's recent survey contains an extensive bibliography together with material on related topics. A forthcoming text contains most of the details we will omit here, as well as computer programs which implement the techniques.