Reliability in Computing - 1st Edition - ISBN: 9780125056304, 9781483277844

Reliability in Computing

1st Edition

The Role of Interval Methods in Scientific Computing

Editors: Ramon E. Moore
eBook ISBN: 9781483277844
Imprint: Academic Press
Published Date: 28th May 1988
Page Count: 444
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Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms.

The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence.

The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions.

The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.

Table of Contents




1. Computer Arithmetic and Mathematical Software

Arithmetic for Vector Processors

FORTRAN-SC, A FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH: Language Description with Examples

FORTRAN-SC A FORTRAN Extension for Engineering/Scientific

Computation with Access to ACRITH: Demonstration of the Compiler and Sample Programs

Reliable Expression Evaluation in PASCAL-SC

Floating-Point Standards—Theory and Practice

Algorithms for Verified Inclusions—Theory and Practice

Applications of Differentiation Arithmetic

2. Linear and Nonlinear Systems

Interval Acceleration of Convergence

Solving Systems of Linear Interval Equations

Interval Least Squares—A Diagnostic Tool

Existence of Solutions and Iterations for Nonlinear Equations

Interval Method for Algebraic Equations

Error Questions in the Computation of Solution Manifolds of Parametrized Equations

The Enclosure of Solutions of Parameter-Dependent Systems of Equations

3. Optimization

An Overview of Global Optimization Using Interval Analysis

Philosophy and Practicalities of Interval Arithmetic

Some Recent Aspects of Interval Algorithms for Global Optimization

The Use of Interval Arithmetic in Uncovering Structure of Linear Systems

4. Operator Equations

The Role of Order in Computing

Interval Methods for Operator Equations

Boundary Implications for Stability Properties: Present Status

Validating Computation in a Function Space

Epilogue: A Poem about My Life, by Daniel J. Langton


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© Academic Press 1988
Academic Press
eBook ISBN:

About the Editor

Ramon E. Moore

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