Scientific computing with automatic result verification : E. Adams and U. Kulisch, Academic Press, Boston, MA, 1993. 612 pp., ISBN 0-120-44210-8.

Abstract

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.