Scientific Computation with Automatic Result Verification
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Home > Computing and Information Technology > Computer science > Mathematical theory of computation > Scientific Computation with Automatic Result Verification: (6 Computing Supplementa)
Scientific Computation with Automatic Result Verification: (6 Computing Supplementa)

Scientific Computation with Automatic Result Verification: (6 Computing Supplementa)


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About the Book

This computing supplementum collects a number of original contributions which all aim to compute rigorous and reliable error bounds for the solution of numerical problems. An introductory article by the editors about the meaning and diverse methods of automatic result verification is followed by 16 original contributions. The first chapter deals with automatic result verification for standard mathematical problems, such as enclosing the solution of ordinary boundary value problems, linear programming problems, linear systems of equations and eigenvalue problems. The second chapter deals with applications of result verification methods to problems of the technical sciences. The contributions consider critical bending vibrations stability tests for periodic differential equations, geometric algorithms in the plane, and the periodic solution of the oregonator, a mathematical model in chemical kinetics. The contributions of the third chapter are concerned with extending and developing the tools required in scientific computation with automatic result verification.

Table of Contents:
Automatic Result Verification.- I. Numerical Methods with Result Verification.- A Method for Producing Verified Results for Two-point Boundary Value Problems.- A Kind of Difference Method for Enclosing Solutions of Ordinary Linear Boundary Value Problems.- A Self-validating Method for Solving Linear Programming Problems with Interval Input Data.- Enclosing the Solutions of Linear Equations by Interval Iterative Processes.- Errorbounds for Quadratic Systems of Nonlinear Equations Using the Precise Scalar Product.- Inclusion of Eigenvalues of General Eigenvalue Problems of Matrices.- Verified Inclusion for Eigenvalues of Certain Difference and Differential Equations.- II. Applications in the Technical Sciences.- VIB — Verified Inclusions of Critical Bending Vibrations.- Stability Test for Periodic Differential Equations on Digital Computers with Applications.- The Periodic Solutions of the Oregonator and Verification of Results.- On Arithmetical Problems of Geometric Algorithms in the Plane.- III. Improving the Tools.- Precise Evaluation of Polynomials in Several Variables.- Evaluation of Arithmetic Expressions with Guaranteed High Accuracy.- Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy.- Inverse Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy.- Inclusion Algorithms with Functions as Data.- FORTRAN-SC. A Study of a FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH.


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Product Details
  • ISBN-13: 9783211820636
  • Publisher: Springer Verlag GmbH
  • Publisher Imprint: Springer Verlag GmbH
  • Height: 244 mm
  • No of Pages: 244
  • Returnable: N
  • Width: 170 mm
  • ISBN-10: 3211820639
  • Publisher Date: 25 Oct 1988
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 6 Computing Supplementa


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