Scientific Computing, Validated Numerics, Interval Methods / Edition 1

by Walter Krämer, Jürgen Wolff von Gudenberg

Overview

Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.

Product Details

ISBN-13:	9781441933768
Publisher:	Springer US
Publication date:	12/01/2010
Edition description:	Softcover reprint of the original 1st ed. 2001
Pages:	398
Product dimensions:	6.69(w) x 9.61(h) x 0.28(d)

Table of Contents

SCAN 2000 Keynote Address The Future of Intervals.- I Software- and Hardware-Tools.- Variable-Precision Exponential Evaluation.- Fast computation of some special integrals of mathematical physics.- Interval Input and Output.- A Case for Interval Hardware on Superscalar Processors.- Evaluating the Impact of Accurate Branch Prediction on Interval Software.- Automatic Test Case Generation using Interval Arithmetic.- II Linear Algebra.- On the Hull of the Solution Sets of Interval Linear Equations.- Computation of Algebraic Solutions to Interval Systems via Systems of Coordinates.- Towards Diagrammatic Analysis of Systems of Interval “Linear Equations”.- On the Solution of Parametrised Linear Systems.- III Polynomials.- Verified solutions of systems of nonlinear polynomial equations.- Euler-like method with Weierstrass’ correction.- IV Set Enclosures.- Guaranteed Set Computation with Subpavings.- A New Intersection Algorithm for Parametric Surfaces Based on LIEs.- State estimation using interval constraint propagation.- V Global Optimization.- Interval Methods for Global Optimization Using the Boxing Method.- A Branch-and-Prune Method for Global Optimization.- Simulation of a Controlled Aircraft Elevator under Sensor Uncertainties.- VI Control.- Traditional parameter estimation versus estimation of guaranteed parameter sets.- Stabilizing Control Design of Nonlinear Process Involving Uncertainties.- Set Estimation, Computation of Volumes and Data Safety.- VII ODE and DAE and Applications.- Verified High-Order Integration of DAEs and Higher-order ODEs.- About a Finite Dimensional Reduction Method for Conservative Dynamical Systems and its Applications.- Verified Determination of Singularities in Chemical Processes.- Modeling of Multibody Systems with IntervalArithmetic.- VIII Shastics and Probability.- On the Algebraic Properties of Shastic Arithmetic. Comparison to Interval Arithmetic.- Global Random Walk Simulations of Diffusion.- Interval Computations as a Particular Case of a General Scheme Involving Classes of Probability Distributions.- For reliable and powerful scientific computations.- Reliable representations of strange attractors.- Appendix: The Referees.