A New Approach to Scientific Computation

Ulrich W. Kulisch, Willard L. Miranker

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780124286603
• eBook ISBN:
  9781483272047
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

A New Approach to Scientific Computation is a collection of papers delivered at a symposium held at the IBM Thomas J. Watson Research Center on August 3, 1982. The symposium provided a forum for reviewing various aspects of an approach to scientific computation based on a systematic theory of computer arithmetic. Computer demonstration packages for standard problems of numerical mathematics are considered. Comprised of 12 chapters, this volume begins by summarizing an extensive research activity in scientific computation as well as the experience gained through various implementations of a new approach to arithmetic on diverse processors, including even microprocessors. A complete listing of the spaces that occur in numerical computations is presented, followed by a discussion of aspects of traditional computer arithmetic and a new definition of computer arithmetic. The properties of semimorphisms are also considered. Subsequent chapters focus on potential applications of programming packages to standard problems in numerical analysis implemented on a Z80 based minicomputer, with a PASCAL extension called PASCAL-SC as the programming language; methods for solving algebraic problems with high accuracy; and the use of a computer with floating-point arithmetic to obtain guaranteed sharp bounds for the value of an arithmetic expression. An extension of FORTRAN which satisfies contemporary requirements of numerical computation is also described. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.

Table of contents

• Front Cover
• A New Approach to Scientific Computation
• Copyright Page
• Table of Contents
• Dedication
• Contributors
• Preface
• Acknowledgments
• CHAPTER 1. A NEW ARITHMETIC FOR SCIENTIFIC COMPUTATION
• CHAPTER 2. COMPUTER DEMONSTRATION PACKAGES FOR STANDARD PROBLEMS OF NUMERICAL MATHEMATICS
• CHAPTER 3. SOLVING ALGEBRAIC PROBLEMS WITH HIGH ACCURACY
• CHAPTER 4. EVALUATION OF ARITHMETIC EXPRESSION SWITH MAXIMUM ACCURACY
• CHAPTER 5. SOLVING FUNCTION SPACE PROBLEMS WITH GUARANTEED CLOSE BOUNDS
• CHAPTER 6. ULTRA-ARITHMETIC: THE DIGITAL COMPUTER SET IN FUNCTION SPACE
• CHAPTER 7. A FORTRAN EXTENSION FOR SCIENTIFIC COMPUTATION
• CHAPTER 8. AN INTRODUCTION TO MATRIX PASCAL:A PASCAL EXTENSION FOR SCIENTIFIC COMPUTATION
• CHAPTER 9. REALIZATION OF AN OPTIMAL COMPUTER ARITHMETIC
• CHAPTER 10. FEATURES OF A HARDWARE IMPLEMENTATION OF AN OPTIMAL ARITHMETIC
• CHAPTER 11. DIFFERENTIATION AND GENERATION OF TAYLOR COEFFICIENTS IN PASCAL-SC
• CHAPTER 12. MATRIX PASCALt