Computer Arithmetic and Validity : : Theory, Implementation, and Applications / / Ulrich Kulisch.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Kulisch, Ulrich,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2013]; ©2012
• Year of Publication: 2013
• Language: English
• Series: De Gruyter Studies in Mathematics , 33
• Physical Description: 1 online resource (434 p.)

This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.

Table of Contents

Frontmatter -- Foreword to the second edition -- Preface -- Contents -- Introduction -- Part I. Theory of computer arithmetic -- Chapter 1. First concepts -- Chapter 2. Ringoids and vectoids -- Chapter 3. Definition of computer arithmetic -- Chapter 4. Interval arithmetic -- Part II. Implementation of arithmetic on computers -- Chapter 5. Floating-point arithmetic -- Chapter 6. Implementation of floating-point arithmetic on a computer -- Chapter 7. Hardware support for interval arithmetic -- Chapter 8. Scalar products and complete arithmetic -- Part III. Principles of verified computing -- Chapter 9. Sample applications -- Appendix A. Frequently used symbols -- Appendix B. On homomorphism -- Bibliography -- List of figures -- List of tables -- Index