Interval Mathematics 1980 - 1st Edition - ISBN: 9780125188500, 9781483273846

Interval Mathematics 1980

1st Edition

Editors: Karl L. E. Nickel
eBook ISBN: 9781483273846
Imprint: Academic Press
Published Date: 1st January 1980
Page Count: 570
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Description

Interval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some of the most important work done in the field of interval mathematics and its application to computing. Topics covered range from purely theoretical to computational methods and computer architecture.

Comprised of 41 chapters, this book begins with an overview of set functions and their applications, followed by a discussion on global constrained optimization using interval analysis. A model for the propagation of rounding error in floating arithmetic is then presented, and the importance of 3-valued notions for interval mathematics is highlighted. Subsequent chapters focus on the transformation of interval programs into convergent interval programs; specifications for interval programming languages; interval contractions for the solution of integral equations; and mean convergence enclosing of solutions of operator equations with convex and inverse monotonic operators.

This monograph will be of value to both students and specialists in the fields of mathematics and computer science.

Table of Contents


Contributors

Foreword

Preface

Invited Lectures

Set Functions and Applications

Global Constrained Optimization Using Interval Analysis

A Model for the Propagation of Rounding Error in Floating Arithmetic

The Importance of 3-Valued Notions for Interval Mathematics

Interval Arithmetic Options in the Proposed IEEE Floating Point Arithmetic Standard

Interval Components of Non-Archimedean Number Systems

Interval Differential Equations

New Results on Nonlinear Systems

Optimal Approximations in Interval Analysis

Some Topics of Segment Analysis

Rounding Error in Gaussian Elimination of Tridiagonal Linear Systems. Survey of Results

Contributed Lectures

On Sets of Solutions of Collections of Nonlinear Systems in IRn

About the Transformation of Interval Programs into Convergent Interval Programs

Specifications for Interval Programming Languages

Interval Contractions for the Solution of Integral Equations

Rounding Invariant Structures by Application of a Mapping of a Ringoid in an Ordered Set

SIGLA-PL/1. Development and Applications

Totally Nonnegative Interval Matrices

Using Scalar and Vector Majorizing Equations to Bound Solution Sets of Nonlinear Algebraic Equation Systems

Application of Interval Analysis to Linear Problems of Optimal Control with Quadratic Cost Functional

Interpolation of Interval-Valued Functions with Restrictions

A Programming System for Interval Arithmetic in ALGOL 68

Extended Circular Arithmetic, Problems and Results

Locating Safe Starting Regions for Iterative Methods: A Heuristic Algorithm

Comparison of Diverse Iteration Methods for Sets

On Discrete Equations, Inequalities, and Interval Evaluations of Fixed Points of Isotone-Antitone Mappings

Evaluation of Complex Logarithms and Related Functions with Interval Arithmetic

Linear Transformations of Vector Sets and Their Applications

Bounding Eigenvectors of a Symmetric Matrix

Computing the Exponential of an Essentially Nonnegative Matrix

Convergent-Optimal Roundings in Totally Ordered Sets

On the Generalization of Some Algorithms for the Simultaneous Approximation of Polynomial Roots

On a Representation of the k-th Root in Complex Circular Interval Arithmetic

A Generalization of the Krawczyk-Moore Algorithm

Optimization of Interval Computation

Optimality of the Centered Form

Interval Power Series

Duality in Interval Linear Programming

Mean Convergence Enclosing of Solutions of Operator Equations with Convex and Inverse Monotonic Operators

Domains with all Solutions of Nonlinear Problems with Non-Inverse-Isotonic Operators

Floating Point Exception Handling for Interval Arithmetic


Details

No. of pages:
570
Language:
English
Copyright:
© Academic Press 1980
Published:
Imprint:
Academic Press
eBook ISBN:
9781483273846

About the Editor

Karl L. E. Nickel