Interval Mathematics 1980
eBook - PDF

Interval Mathematics 1980

  1. 570 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Interval Mathematics 1980

Book details
Table of contents
Citations

About This Book

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.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483273846
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics

Table of contents

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