Scientific Computing, Validated Numerics, Interval Methods

by Kramer, Walter; Gudenberg, Jurgen Wolff Von

• ISBN13: 9780306467066
• ISBN10: 0306467062
• Format: Hardcover
• Copyright: 2001-12-01
• Publisher: Plenum Pub Corp

Summary

The papers in this book discuss a wide variety of serious applications of all parts of mathematical modelling. New efficient, publicly available or even commercial tools are proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened. They are concerned not only with applications of well known enclosure methods or the development of new-self validating algorithms, but also transfer the mechanisms and design process known from these areas to other fields. The 31 contributions to this proceedings volume were carefully selected from a much larger number of submissions.

Table of Contents

SCAN 2000 Keynote Address The Future of Intervals	p. 1
Software-- and Hardware--Tools
Variable-Precision Exponential Evaluation	p. 19
Fast computation of some special integrals of mathematical physics	p. 29
Interval Input and Output	p. 41
A Case for Interval Hardware on Superscalar Processors	p. 53
Evaluating the Impact of Accurate Branch Prediction on Interval Software	p. 69
Automatic Test Case Generation using Interval Arithmetic	p. 81
Linear Algebra
On the Hull of the Solution Sets of Interval Linear Equations	p. 91
Computation of Algebraic Solutions to Interval Systems via Systems of Coordinates	p. 103
Towards Diagrammatic Analysis of Systems of Interval "Linear Equations"	p. 115
On the Solution of Parametrised Linear Systems	p. 127
Polynomials
Verified solutions of systems of nonlinear polynomial equations	p. 141
Euler-like method with Weierstrass' correction	p. 153
Set Enclosures
Guaranteed Set Computation with Subpavings	p. 167
A New Intersection Algorithm for Parametric Surfaces Based on LIEs	p. 179
State estimation using interval constraint propagation	p. 191
Global Optimization
Interval Methods for Global Optimization Using the Boxing Method	p. 205
A Branch-and-Prune Method for Global Optimization	p. 215
Simulation of a Controlled Aircraft Elevator under Sensor Uncertainties	p. 227
Control
Traditional parameter estimation versus estimation of guaranteed parameter sets	p. 241
Stabilizing Control Design of Nonlinear Process Involving Uncertainties	p. 255
Set Estimation, Computation of Volumes and Data Safety	p. 267
ODE and DAE and Applications
Verified High-Order Integration of DAEs and Higher-order ODEs	p. 281
About a Finite Dimensional Reduction Method for Conservative Dynamical Systems and its Applications	p. 293
Verified Determination of Singularities in Chemical Processes	p. 305
Modeling of Multibody Systems with Interval Arithmetic	p. 317
Stochastics and Probability
On the Algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic	p. 331
Global Random Walk Simulations of Diffusion	p. 343
Interval Computations as a Particular Case of a General Scheme Involving Classes of Probability Distributions	p. 355
For reliable and powerful scientific computations	p. 367
Reliable representations of strange attractors	p. 379
The Referees	p. 391
Index	p. 393
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