Interval Analysis: Introduction, Methods and Applications ( Mathematics Research Developments )

Publication series :Mathematics Research Developments

Author: Walter N. Osborne  

Publisher: Nova Science Publishers, Inc.‎

Publication year: 2017

E-ISBN: 9781536120493

P-ISBN(Paperback): 9781536120288

Subject: O241 数值分析

Keyword: 数值分析

Language: ENG

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Interval Analysis: Introduction, Methods and Applications

Chapter

Chapter 2

Interval Methods of Global Constrained Optimization

Abstract

Introduction

Definitions and Notations

Intervals and Interval Vectors

Interval Arithmetic

Interval Function Extension

Inverter

Interval Minimization Problem Statement

Inversed Interval Optimization Algorithms

Method of Direct Image Dichotomy

Step-by-Step Description of the Algorithm

Parameter Influence

Method of Virtual Values Cutoff

Step-by-Step Description of the Algorithm

Parameter Influence

Method of Virtual Values Stochastic Cutoff

Step-by-Step Description of the Algorithm

Parameter Influence

Method of Stochastic Pullout

Step-by-Step Description of the Algorithm

Parameter Influence

Generalized Inversed Method

Check Operator Algorithms

Compress Operator Algorithms

Step-by-Step Description of the Generalized Inversed Method

Parameter Influence

Meta-Heuristic Optimization Algorithms

Method of Average Path Endings

Step-by-Step Description of the Algorithm

Parameter Influence

Method of Stochastic Grid

Step-by-Step Description of the Algorithm

Parameter Influence

Interval Scatter Search

Step-by-Step Description of the Algorithm

Parameter Influence

Interval Genetic Algorithm (IGA)

Step-by-Step Description of the Algorithm

Parameter Influence

Interval Explosion Search (IES)

Step-by-Step Description of the Algorithm

Parameter Influence

Adaptive Interval Algorithm (AIA)

Step-by-Step Description of the Algorithm

Appendix to Adaptive Interval Algorithm

Parameter Influence

Self-Organizing Interval Bacterial Colony Evolution Algorithm (SOIBCEA)

Step-by-Step Description of the Algorithm

Appendix to SOIBCEA

Point Generation Procedures

Parameter Influence

Optimization Benchmark Tests

Technical System Design Problems

Welded Beam Design

High Pressure Vessel Design

Speed Reducer Design

Tension/Compression Spring Design

Conclusion

Acknowledgment

References

Chapter 3

Applications of Interval Analysis in Computer Graphics

Abstract

Introduction

Applications of Interval Computations in Computer Graphics

Possible Future Applications of Interval Computations in Computer Graphics

References

Chapter 4

Workspace Analysis and Design of Cable-Driven Parallel Manipulators

Abstract

1. Introduction

2. Interval Solving of Wrench-Feasibility

2.1. The Equilibrium in Its Interval Form

2.2. Wrench-Feasibility of the Equilibrium

3. Workspace Analysis of Cable Robots

4. Design of Cable Robots for a Desired Workspace

Conclusion

References

Index

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