Applications of interval computations:
Applications of Interval Computations contains primarily survey articles of actual, industrial applications of numerical analysis with automatic result verification and of interval representation of data. Underlying topics include branch and bound algorithms for global optimization, constraint propa...
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Applied optimization
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Applications of Interval Computations contains primarily survey articles of actual, industrial applications of numerical analysis with automatic result verification and of interval representation of data. Underlying topics include branch and bound algorithms for global optimization, constraint propagation, solution sets of linear systems, hardware and software systems for interval computations, and fuzzy logic. Actual applications described in the book include economic input-output models, quality control in manufacturing design, a computer-assisted proof in quantum mechanics, medical expert systems, and others. A realistic view of interval computations is taken: the articles indicate when and how over-estimation and other challenges can be overcome. An introductory chapter explains the content of the papers in terminology accessible to mathematically literate graduate students The style of the individual, refereed contributions has been made uniform and understandable, and there is an extensive book-wide index. The book should be valuable to students and researchers interested in automatic result verification |
| Physical Description: | XVII, 425 S. Ill., graph. Darst. |
| ISBN: | 0792338472 |
Staff View
MARC
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| 490 | 1 | |a Applied optimization |v 3 | |
| 520 | 3 | |a Applications of Interval Computations contains primarily survey articles of actual, industrial applications of numerical analysis with automatic result verification and of interval representation of data. Underlying topics include branch and bound algorithms for global optimization, constraint propagation, solution sets of linear systems, hardware and software systems for interval computations, and fuzzy logic. Actual applications described in the book include economic input-output models, quality control in manufacturing design, a computer-assisted proof in quantum mechanics, medical expert systems, and others. A realistic view of interval computations is taken: the articles indicate when and how over-estimation and other challenges can be overcome. An introductory chapter explains the content of the papers in terminology accessible to mathematically literate graduate students | |
| 520 | |a The style of the individual, refereed contributions has been made uniform and understandable, and there is an extensive book-wide index. The book should be valuable to students and researchers interested in automatic result verification | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE xiii
1 APPLICATIONS OF INTERVAL
COMPUTATIONS: AN INTRODUCTION
R. Baker Kearfott and Vladik Kreinovich 1
1 What are Interval Computations? 1
2 International Workshop on Applications of Interval
Computations: How This Book Originated 8
3 General Optimization Problems 10
4 General Systems of Equations and Inequalities 14
5 Linear Interval Problems 15
6 Interval Computations Can Also Handle Possible Additional
Information About the Input Data 18
7 Software and Hardware Support for Interval Computations 20
REFERENCES 21
2 A REVIEW OF TECHNIQUES IN THE
VERIFIED SOLUTION OF CONSTRAINED
GLOBAL OPTIMIZATION PROBLEMS
R. Baker Kearfott 23
1 Introduction, Basic Ideas and Literature 23
2 On Constrained Optimization Problems 32
3 On Use of Interval Newton Methods 40
4 Applications 52
5 Summary and Present Work 53
REFERENCES 54
vi Applications of Interval Computations
3 THE SHAPE OF THE SYMMETRIC
SOLUTION SET
Gdiz Alefeld, Vladik Kreinovich, and Giinter Mayer 61
1 Introduction 61
2 Notation 62
3 Results 63
4 Examples 74
REFERENCES 79
4 LINEAR INTERVAL EQUATIONS:
COMPUTING ENCLOSURES WITH
BOUNDED RELATIVE OVERESTIMATION
IS NP HARD
JifiRohn 81
1 Introduction 81
2 The Result 82
3 The Symmetric Case 86
4 Concluding Remark 87
REFERENCES 88
5 QUALITY IMPROVEMENT VIA
OPTIMIZATION OF TOLERANCE
INTERVALS DURING THE DESIGN STAGE
Sevgui Hadjihassan, Eric Walter, and Luc Pronzato 91
1 Introduction 91
2 Some Basic Models, and their Origins 97
3 Model of Performance Characteristic is Known Beforehand 101
4 Model Parameters Estimated in Controlled Conditions 111
5 Controlled Conditions are Unavailable 117
6 Temperature Controller 123
7 Conclusions 126
REFERENCES 128
Contents vii
6 APPLICATIONS OF INTERVAL
COMPUTATIONS TO REGIONAL
ECONOMIC INPUT OUTPUT MODELS
Max E. Jerrell 133
1 Economic Input Output Models 133
2 Technical Coefficients are Only Known with Uncertainty 135
3 Statistical Methods are Not Directly Applicable, Hence,
Interval Computations May Be Useful 136
4 Computational Algorithms 138
5 An Example 140
REFERENCES 142
7 INTERVAL ARITHMETIC IN QUANTUM
MECHANICS
Charles L. Fefferman and Luis A. Seco 145
1 Quantum Mechanics 146
2 Computer Assisted Set up 151
3 The Thomas Fermi Equation 154
4 The Aperiodicity Inequality 160
REFERENCES 164
8 INTERVAL COMPUTATIONS ON THE
SPREADSHEET
Eero Hyvonen and Stefano De Pascale 169
1 Limitations of Spreadsheet Computing 169
2 Extended IA on a Spreadsheet 174
3 Global IA on a Spreadsheet 184
4 Interval Constraint Spreadsheets 195
5 Discussion 204
REFERENCES 205
9 SOLVING OPTIMIZATION PROBLEMS
WITH HELP OF THE UNICALC SOLVER
Alexander L. Semenov 211
1 Introduction 211
2 The UniCalc Solver 212
viii Applications of Interval Computations
3 The Algorithm of Sub definite Calculations 213
4 Solving Integer Programming Problems 219
5 Real Valued Optimization 221
6 Future Developments 223
REFERENCES 224
10 AUTOMATICALLY VERIFIED
ARITHMETIC ON PROBABILITY
DISTRIBUTIONS AND INTERVALS
Daniel Berleant 227
1 Introduction 227
2 Correctly Representing PDFs and Intervals with His¬
tograms 229
3 Arithmetic Operations 232
REFERENCES 243
11 NESTED INTERVALS AND SETS:
CONCEPTS, RELATIONS TO FUZZY SETS,
AND APPLICATIONS
Hung T. Nguyen and Vladik Kreinovich 245
1 Introduction 246
2 Nested Intervals and Nested Sets 250
3 Other Problems Where Nested Sets and Nested Intervals
Can Be Used: Identification, Optimization, Control, and
Decision Making 267
4 Applications of Nested Sets and Nested Intervals 273
APPENDIX A Proofs 279
REFERENCES 283
12 FUZZY INTERVAL INFERENCE UTILIZING
THE CHECKLIST PARADIGM AND
BK RELATIONAL PRODUCTS
Ladislav J. Kohout and Wyllis Bandler 291
1 Introduction 291
2 Many Valued Logics for Interval Fuzzy Inference Based on
the Checklist Paradigm 293
3 Groups of Logic Transformations of Interval Connectives 310
Contents ix
4 Special Types of Compositions of Relations 314
5 An Application: The Basic Knowledge Handling
Mechanisms of CLINAID by Means of Relational Inference 321
6 Toward Successful Utilization of Interval Methods in Soft
Computing 328
REFERENCES 329
13 COMPUTING UNCERTAINTY IN
INTERVAL BASED SETS
Luis Mateus Rocha, Vladik Kreinovich, and R. Baker Kearfott 337
1 Introduction 337
2 Evidence Sets as a Description of Uncertainty 338
3 Different Measures of Uncertainty, and How to Describe
them Numerically 355
4 L—Fuzzy Sets, Interval Based L—Fuzzy Sets, and
L Evidence Sets 370
5 3 D Uncertainty Unit Cube 374
REFERENCES 377
14 SOFTWARE AND HARDWARE
TECHNIQUES FOR ACCURATE,
SELF VALIDATING ARITHMETIC
Michael J. Schulie and Earl E. Swarizlander, Jr. 381
1 Introduction 381
2 Software Tools 383
3 Hardware Designs 388
4 A Variable Precision, Interval Arithmetic Coprocessor 391
5 Conclusions and Areas for Future Research 396
REFERENCES 398
15 STIMULATING HARDWARE AND
SOFTWARE SUPPORT FOR INTERVAL
ARITHMETIC
G. William Walster 405
1 Introduction 405
2 The Participants 406
3 Stable Equilibrium 410
x Applications of Interval Computations
4 The Interval Paradigm Shift 411
5 System Supplier Demand 412
6 End user Demand 412
7 Action Plan 414
REFERENCES 415
INDEX 417
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| indexdate | 2024-07-09T18:07:49Z |
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| isbn | 0792338472 |
| language | English |
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| physical | XVII, 425 S. Ill., graph. Darst. |
| publishDate | 1996 |
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| series | Applied optimization |
| series2 | Applied optimization |
| spelling | Applications of interval computations ed. by R. Baker Kearfott ... Dordrecht [u.a.] Kluwer 1996 XVII, 425 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 3 Applications of Interval Computations contains primarily survey articles of actual, industrial applications of numerical analysis with automatic result verification and of interval representation of data. Underlying topics include branch and bound algorithms for global optimization, constraint propagation, solution sets of linear systems, hardware and software systems for interval computations, and fuzzy logic. Actual applications described in the book include economic input-output models, quality control in manufacturing design, a computer-assisted proof in quantum mechanics, medical expert systems, and others. A realistic view of interval computations is taken: the articles indicate when and how over-estimation and other challenges can be overcome. An introductory chapter explains the content of the papers in terminology accessible to mathematically literate graduate students The style of the individual, refereed contributions has been made uniform and understandable, and there is an extensive book-wide index. The book should be valuable to students and researchers interested in automatic result verification Interval analysis (Mathematics) Congresses Intervallalgebra (DE-588)4139152-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Intervallalgebra (DE-588)4139152-4 s DE-604 Kearfott, R. B. Sonstige oth Applied optimization 3 (DE-604)BV010841718 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007608532&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Applications of interval computations Applied optimization Interval analysis (Mathematics) Congresses Intervallalgebra (DE-588)4139152-4 gnd |
| subject_GND | (DE-588)4139152-4 (DE-588)1071861417 |
| title | Applications of interval computations |
| title_auth | Applications of interval computations |
| title_exact_search | Applications of interval computations |
| title_full | Applications of interval computations ed. by R. Baker Kearfott ... |
| title_fullStr | Applications of interval computations ed. by R. Baker Kearfott ... |
| title_full_unstemmed | Applications of interval computations ed. by R. Baker Kearfott ... |
| title_short | Applications of interval computations |
| title_sort | applications of interval computations |
| topic | Interval analysis (Mathematics) Congresses Intervallalgebra (DE-588)4139152-4 gnd |
| topic_facet | Interval analysis (Mathematics) Congresses Intervallalgebra Konferenzschrift |
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