Applications of Interval Computations / edited by R. Baker Kearfott, Vladik Kreinovich
(Applied Optimization ; 3)
| データ種別 | 電子ブック |
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| 出版情報 | Boston, MA : Springer US , 1996 |
| 本文言語 | 英語 |
| 大きさ | XVIII, 428 p : online resource |
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| 内容注記 | 1 Applications of Interval Computations: An Introduction 1 What are Interval Computations? 2 International Workshop on Applications of Interval Computations: How This Book Originated 3 General Optimization Problems 4 General Systems of Equations and Inequalities 5 Linear Interval Problems 6 Interval Computations Can Also Handle Possible Additional Information About the Input Data 7 Software and Hardware Support for Interval Computations References 2 A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems 1 Introduction, Basic Ideas and Literature 2 On Constrained Optimization Problems 3 On Use of Interval Newton Methods 4 Applications 5 Summary and Present Work References 3 The Shape of the Symmetric Solution Set 1 Introduction 2 Notation 3 Results 4 Examples References 4 Linear Interval Equations: Computing Enclosures with Bounded Relative Overestimation is NP-Hard 1 Introduction 2 The Result 3 The Symmetric Case 4 Concluding Remark References 5 Quality Improvement via Optimization of Tolerance Intervals During the Design Stage 1 Introduction 2 Some Basic Models, and their Origins 3 Model of Performance Characteristic is Known Beforehand 4 Model Parameters Estimated in Controlled Conditions 5 Controlled Conditions are Unavailable 6 Temperature Controller 7 Conclusions References 6 Applications of Interval Computations to Regional Economic Input-Output Models 1 Economic Input-Output Models 2 Technical Coefficients are Only Known with Uncertainty 3 Statistical Methods are Not Directly Applicable, Hence, Interval Computations May Be Useful 4 Computational Algorithms 5 An Example References 7 Interval Arithmetic in Quantum Mechanics 1 Quantum Mechanics 2 Computer-Assisted Set-up 3 The Thomas-Fermi Equation 4 The Aperiodicity Inequality References 8 Interval Computations on the Spreadsheet 1 Limitations of Spreadsheet Computing 2 Extended IA on a Spreadsheet 3 Global IA on a Spreadsheet 4 Interval Constraint Spreadsheets 5 Discussion References 9 Solving Optimization Problems with Help of the UniCalc Solver 1 Introduction 2 The UniCalc Solver 3 The Algorithm of Sub definite Calculations 4 Solving Integer Programming Problems 5 Real-Valued Optimization 6 Future Developments References 10 Automatically Verified Arithmetic on Probability Distributions and Intervals 1 Introduction 2 Correctly Representing PDFs and Intervals with Histograms 3 Arithmetic Operations References 11 Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications 1 Introduction 2 Nested Intervals and Nested Sets 3 Other Problems Where Nested Sets and Nested Intervals Can Be Used: Identification, Optimization, Control, and Decision Making 4 Applications of Nested Sets and Nested Intervals Appendix A Proofs References 12 Fuzzy Interval Inference Utilizing the Checklist Paradigm and BK-Relational Products 1 Introduction 2 Many-Valued Logics for Interval Fuzzy Inference Based on the Checklist Paradigm 3 Groups of Logic Transformations of Interval Connectives 4 Special Types of Compositions of Relations 5 An Application: The Basic Knowledge Handling Mechanisms of CLIN AID by Means of Relational Inference 6 Toward Successful Utilization of Interval Methods in Soft Computing References 13 Computing Uncertainty in Interval Based Sets 1 Introduction 2 Evidence Sets as a Description of Uncertainty 3 Different Measures of Uncertainty, and How to Describe them Numerically 4 L-Fuzzy Sets, Interval Based L-Fuzzy Sets, and L-Evidence Sets 5 3-D Uncertainty Unit Cube References 14 Software and Hardware Techniques for Accurate, Self-Validating Arithmetic 1 Introduction 2 Software Tools 3 Hardware Designs 4 A Variable-Precision, Interval Arithmetic Coprocessor 5 Conclusions and Areas for Future Research References 15 Stimulating Hardware and Software Support for Interval Arithmetic 1 Introduction 2 The Participants 3 Stable Equilibrium 4 The Interval Paradigm Shift 5 System Supplier Demand 6 End-user Demand 7 Action Plan References |
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| 一般注記 | Primary Audience for the Book • Specialists in numerical computations who are interested in algorithms with automatic result verification. • Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc cessful applications. • Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli cations of numerical methods with automatic result verification, that were pre sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g |
| 著者標目 | Kearfott, R. Baker editor Kreinovich, Vladik editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Artificial intelligence LCSH:Computer mathematics LCSH:Mathematical models LCSH:Calculus of variations FREE:Mathematics FREE:Mathematical Modeling and Industrial Mathematics FREE:Computational Mathematics and Numerical Analysis FREE:Calculus of Variations and Optimal Control; Optimization FREE:Artificial Intelligence (incl. Robotics) |
| 分 類 | DC23:003.3 |
| 巻冊次 | ISBN:9781461334408 
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| ISBN | 9781461334408 |
| URL | http://dx.doi.org/10.1007/978-1-4613-3440-8 |
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