Interval Mathematics 1980

Karl L. E. Nickel

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780125188500
• eBook ISBN: 9781483273846
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Interval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some of the most important work done in the field of interval mathematics and its application to computing. Topics covered range from purely theoretical to computational methods and computer architecture. Comprised of 41 chapters, this book begins with an overview of set functions and their applications, followed by a discussion on global constrained optimization using interval analysis. A model for the propagation of rounding error in floating arithmetic is then presented, and the importance of 3-valued notions for interval mathematics is highlighted. Subsequent chapters focus on the transformation of interval programs into convergent interval programs; specifications for interval programming languages; interval contractions for the solution of integral equations; and mean convergence enclosing of solutions of operator equations with convex and inverse monotonic operators. This monograph will be of value to both students and specialists in the fields of mathematics and computer science.

Table of contents

• Front Cover
• Interval Mathematics 1980
• Copyright Page
• Table of Contents
• Contributors
• Foreword
• Preface
• CHAPTER 1. SET FUNCTIONS AND APPLICATIONS
• CHAPTER 2. GLOBAL CONSTRAINED OPTIMIZATION USING INTERVAL ANALYSIS
• CAPTER 3. A MODEL FOR THE PROPAGATION OF ROUNDING ERROR IN FLOATING ARITHMETIC
• CAPTER 4. THE IMPORTANCE OF 3-VALUED NOTIONS FOR INTERVAL MATHEMATICS
• CHAPTER 5. INTERVAL ARITHMETIC OPTIONS IN THE PROPOSED IEEE FLOATING POINT ARITHMETIC STANDARD
• CHAPTER 6. INTERVAL COMPONENTS OF NONARCHIMEDEAN NUMBER SYSTEMS
• CHAPTER 7. INTERVAL DIFFERENTIAL EQUATIONS
• Chapter 8. NEW RESULTS ON NONLINEAR SYSTEMS
• CHAPTER 9. OPTIMAL APPROXIMATIONS IN INTERVAL ANALYSIS
• CHAPTER 10. SOME TOPICS OF SEGMENT ANALYSIS
• CHAPTER 11. ROUNDING ERROR IN GAUSSIAN ELIMINATION OF TRIDIAGONAL LINEAR SYSTEMS SURVEY OF RESULTS
• CHAPTER 12. ON SETS OF SOLUTIONS OF COLLECTIONS OF NONLINEAR SYSTEMS IN R
• CHAPTER 13. ABOUT THE TRANSFORMATION OF INTERVAL PROGRAMS INTO CONVERGENT INTERVAL PROGRAMS
• CHAPTER 14. SPECIFICATIONS FOR INTERVAL PROGRAMMING LANGUAGES
• CHAPTER 15. INTERVAL CONTRACTIONS FOR THE SOLUTION OF INTEGRAL EQUATIONS
• CHAPTER 16. ROUNDING INVARIANT STRUCTURES BY APPLICATION OF A MAPPING OF A RINGOID IN AN ORDERED SET
• CHAPTER 17. SIGLA-PL/1 DEVELOPMENT AND APPLICATIONS
• CHAPTER 18. TOTALLY NONNEGATIVE INTERVAL MATRICES
• CHAPTER 19. USING SCALAR AND VECTOR MAJORIZING EQUATIONS TO BOUND SOLUTION SETS OF NONLINEAR ALGEBRAIC EQUATION SYSTEMS
• CHAPTER 20. APPLICATION OF INTERVAL ANALYSIS TO LINEAR PROBLEMS OF OPTIMAL CONTROL WITH QUADRATIC FUNCTIONAL
• CHAPTER 21. INTERPOLATION OF INTERVAL-VALUED FUNCTIONS WITH RESTRICTIONS
• CHAPTER 22. A PROGRAMMING SYSTEM FOR INTERVAL ARITHMETIC
• CHAPTER 23. EXTENDED CIRCULAR ARITHMETIC, PROBLEMS AND RESULTS
• CHAPTER 24. LOCATING SAFE STARTING REGIONS FOR ITERATIVE METHODS: A HEURISTIC ALGORITHM
• CHAPTER 25. COMPARISON OF DIVERSE ITERATION METHODS FOR SETS
• CHAPTER 26. ON DISCRETE EQUATIONS, INEQUALITIES AND INTERVAL EVALUATIONS OF FIXED POINTS OF ISOTONE - ANTITONE MAPPINGS
• CHAPTER 27. EVALUATION OF COMPLEX LOGARITHMS AND RELATED FUNCTIONS WITH INTERVAL ARITHMETIC
• CHAPTER 28. LINEAR TRANSFORMATIONS OF VECTOR SETS AND THEIR APPLICATIONS
• CHAPTER 29. BOUNDING EIGENVECTORS OF A SYMMETRIC MATRIX
• CHAPTER 30. COMPUTING THE EXPONENTIAL OF AN ESSENTIALLY NONNEGATIVE MATRIX
• CHAPTER 31. CONVERGENT-OPTIMAL ROUNDINGS IN TOTALLY ORDERED SETS
• CHAPTER 32. ON THE GENERALIZATION OF SOME ALGORITHMS FOR THE SIMULTANEOUS APPROXIMATION OF POLYNOMIAL ROOTS
• CHAPTER 33. ON A REPRESENTATION OF THE K-TH ROOT IN COMPLEX CIRCULAR INTERVAL ARITHMETIC
• CHAPTER 34. A GENERALIZATION OF THE KRAWCZYK-MOORE ALGORITHM
• CHAPTER 35. OPTIMIZATION OF INTERVAL COMPUTATION
• CHAPTER 36. OPTIMALITY OF THE CENTERED FORM
• CHAPTER 37. INTERVAL POWER SERIES
• CHAPTER 38. DUALITY IN INTERVAL LINEAR PROGRAMMING
• CHAPTER 39. MEAN CONVERGENCE ENCLOSING OF SOLUTIONS OF OPERATOR EQUATIONS WITH CONVEX AND INVERSE MONOTONIC OPERATORS
• CHAPTER 40. DOMAINS WITH ALL SOLUTIONS OF NON-LINEAR PROBLEMS WITH NON-INVERSE-ISOTONIC OPERATORS
• CHAPTER 41. FLOATING POINT EXCEPTION HANDLING FOR INTERVAL ARITHMETIC