Reliability in Computing
The Role of Interval Methods in Scientific Computing
Published on 1. July 1988
Book
Hardback
444 pages
978-0-12-505630-4 (ISBN)
Description
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.
More details
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Professional and scholarly
Weight
780 gr
ISBN-13
978-0-12-505630-4 (9780125056304)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
05/2014
Academic Press
€54.95
Available for download
Content
Contributors
Preface
Acknowledgments
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
Preface
Acknowledgments
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