Prentice-Hall, Inc., 1963 - 161 p.The development of automatic digital computers has made it possible to carry out computations involving a very large number of arithmetic operations and this has stimulated a study of the cumulative effect of rounding errors. In this book I have given an elementary introduction to this subject which is based on the work which has been done in the Mathematics Division of N.P.L. in the past few years. Some of the material presented here has already appeared in published papers, but much of it has hitherto been available only in the form of rough notes for lectures given in this country and the United States. Error analysis is regarded by many users of digital computers as a subject for experts. This view is probably the result of attempting to read, at widely separated intervals, isolated analyses presented from entirely different standpoints. In this book I have attempted to present a number of simple analyses in a uniform manner. This has made it necessary to be somewhat selective in the choice of material but it is hoped that, in spite of this, the analyses are reasonably representative. It is my hope that in this way the ideas will be readily assimilated by anyone who can understand the techniques which are analysed. The first draft was read and criticized helpfully by a number of colleagues in Mathematics Division and I am particularly indebted to E. T. Goodwin and D. W. Martin. I would also like to thank G. E. Forsythe, Director of the Computation Center, Stanford, for numerous helpful suggestions. I am very grateful to Mrs. I. Goode for her invaluable assistance in seeing the book through the press.CONTENTS. THE FUNDAMENTAL ARITHMETIC OPERATIONS. COMPUTATIONS INVOLVING POLYNOMIALS. MATRIX COMPUTATIONS. Additional comments. BIBLIOGRAPHY. INDEX.
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