Reliability in Computing
The Role of Interval Methods in Scientific Computing
Published on 10. May 2014
444 pages
978-1-4832-7784-4 (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.
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07/1988
Academic Press
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Content
ContributorsPrefaceAcknowledgments1. 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 Arithmetic2. 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 Equations3. 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 Systems4. 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
