E-raamat: Applications of Interval Computations

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 Describethem 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.