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Interval mathematics 1980 : proceedings of an International Symposium on Interval Mathematics, held at the Institut f�ur Angewandte Mathematik, Universit�at Freiburg i. Br., Germany, May 27-31, 1980. /
| Clasificación: | Libro Electrónico |
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| Autor Corporativo: | |
| Otros Autores: | |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1980.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Interval Mathematics 1980; Copyright Page; Table of Contents; Contributors; Foreword; Preface; CHAPTER 1. SET FUNCTIONS AND APPLICATIONS; I. INTRODUCTION; II. DEFINITIONS AND BASIC THEOREMS; III. SET FUNCTIONS; IV. APPLICATIONS; REFERENCES; CHAPTER 2. GLOBAL CONSTRAINED OPTIMIZATION USING INTERVAL ANALYSIS; I. INTRODUCTION; II. FEASIBILITY; III. AN UPPER BOUND; IV. MONOTONICITY; V. NONCONVEXITY; VI. NEWTON'S METHOD; VII. USE OF AN UPPER BOUND; VIII. USE OF CONSTRAINTS; IX. INTERVAL INEQUALITIES; X. ELIMINATION; XI. THE SEARCH FOR PIVOTS; XII. SOLVING INTERVAL INEQUALITIES
- XIII. IMPROVING THE UPPER BOUNDXIV. FINDING A VERTEX; XV. A LINE SEARCH; XVI. TERMINATION; XVII. BOUNDING f* BUT NOT x; XVIII. A DIFFICULTY; XIX. LINEAR PROGRAMMING; XX. INTEGER PROGRAMMING; XXI. THE INITIAL REGION; REFERENCES; CAPTER 3. A MODEL FOR THE PROPAGATION OF ROUNDING ERROR IN FLOATING ARITHMETIC; I. INTRODUCTION; II. AN EXAMPLE; III. THE MODEL: NOTATION; IV. THE MODEL: AXIOMS; V. THE MODEL: ALGORITHMS; VI. EXAMPLE: EVALUATION OF A SUM; VII. EXAMPLE: LENGTH OF A POLYGON; VIII. EXAMPLE: A RECURRENCE RELATION; IX. A DISCLAIMER; BIBLIOGRAPHY
- CAPTER 4. THE IMPORTANCE OF 3-VALUED NOTIONS FOR INTERVAL MATHEMATICSI. 3-VALUED ORDER RELATIONS; II. RECURSIVE CONSTRUCTION OF INTERVAL ARITHMETIC; III. 3-VALUED ANALYSIS; IV. SHORT SURVEY OF ADDITIONAL POSSIBILITIES TO APPLY 3-VALUED NOTIONS; REFERENCES; CHAPTER 5. INTERVAL ARITHMETIC OPTIONS IN THE PROPOSED IEEE FLOATING POINT ARITHMETIC STANDARD; I. ABSTRACT; II. INTRODUCTION; III. CONTROVERSY AND MISCONCEPTIONS; IV. ANTITHEOREMS; V. THE ANTI-THEOREMS' IMPACT; VI. WHAT IS GRADUAL UNDERFLOW?; ANNOTATED BIBLIOGRAPHY; CHAPTER 6. INTERVAL COMPONENTS OF NONARCHIMEDEAN NUMBER SYSTEMS
- I. INTRODUCTIONII. HESSENBERG OPERATIONS; III. RATIONAL ORDINAL NUMBERS; IV. INTERVAL COMPONENTS; V. TRANSFINITE REAL INTERVAL NUMBERS; REFERENCES; INTERVAL DIFFERENTIAL EQUATIONS; CHAPTER 7. INTERVAL DIFFERENTIAL EQUATIONS; I. INTRODUCTION; II. DIFFERENTIATION OF INTERVAL FUNCTION OF A REAL VARIABLE; III. INTEGRATION AND DIFFERENTIATION; IV. THE INTERVAL DIFFERENTIAL EQUATION X'
- F(t, X); V. EXTENDED SEGMENT ANALYSIS; REFERENCES; Chapter 8. NEW RESULTS ON NONLINEAR SYSTEMS; I. INTRODUCTION; II. EXISTENCE; III. CONVERGENCE; IV. SEARCH PROCEDURES; V. EXPLOITING STRUCTURE
- VI. OTHER NEW DEVELOPMENTSACKNOWLEDGMENTS; REFERENCES; CHAPTER 9. OPTIMAL APPROXIMATIONS IN INTERVAL ANALYSIS; I. INTERVAL ANALYTIC APPROXIMATIONS; III. EXAMPLES; REFERENCES; CHAPTER 10. SOME TOPICS OF SEGMENT ANALYSIS; 1. SEGMENT ARITHMETIC; 2. SEGMENT SEQUENCES; 3. SEGMENT FUNCTIONS; 5. CONVERGENCE OF DERIVATIVES OF LINEAR OPERATORS; REFERENCES; CHAPTER 11. ROUNDING ERROR IN GAUSSIAN ELIMINATION OF TRIDIAGONAL LINEAR SYSTEMS SURVEY OF RESULTS; INTRODUCTION; I. BASIC NOTIONS; II. DATA AND RESIDUAL CONDITION NUMBERS; III. GAUSSIAN ELIMINATION; IV. TWO-SIDED ELIMINATION; V. NUMERICAL EXAMPLE