Scientific Computing, Validated Numerics, Interval Methods

Inbunden, Engelska, 2001

AvWalter Kramer,Richard N. Arteca,Walter Krämer,Jürgen Wolff von Gudenberg,Jürgen Wolff Von Gudenberg,Jürgen Wolff von Gudenberg

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The papers in this book discuss a wide variety of serious applications of all parts of mathematical modelling. Efficient, publicly available, or even commercial tools are proposed or presented, and also, foundations of the theory of intervals and reliable computations are considerably strengthened. The book is 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 volume were carefully selected from a much larger number of submissions.

Produktinformation

Utgivningsdatum2001-12-31
Mått178 x 254 x 27 mm
Vikt969 g
FormatInbunden
SpråkEngelska
Antal sidor398
Upplaga2001
FörlagSpringer Science+Business Media
ISBN9780306467066

Tillhör följande kategorier

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 Stochastics and Probability.- On the Algebraic Properties of Stochastic 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.