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About this book
This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Methods and Applications of Error-Free Computation
Authors: R. T. Gregory, E. V. Krishnamurthy
Series Title: Monographs in Computer Science
DOI: https://doi.org/10.1007/978-1-4612-5242-9
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag New York Inc. 1984
Softcover ISBN: 978-1-4612-9754-3Published: 26 September 2011
eBook ISBN: 978-1-4612-5242-9Published: 06 December 2012
Series ISSN: 0172-603X
Series E-ISSN: 2512-5486
Edition Number: 1
Number of Pages: 194
Topics: Numerical Analysis, Computational Science and Engineering, Arithmetic and Logic Structures