Reliability in Computing

Reliability in Computing

The Role of Interval Methods in Scientific Computing

1st Edition - May 28, 1988

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  • Editor: Ramon E. Moore
  • eBook ISBN: 9781483277844

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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

  • Contributors



    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

Product details

  • No. of pages: 444
  • Language: English
  • Copyright: © Academic Press 1988
  • Published: May 28, 1988
  • Imprint: Academic Press
  • eBook ISBN: 9781483277844

About the Editor

Ramon E. Moore

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