Error Control and Adaptivity in Scientific Computing

✍ Scribed by G. Alefeld (auth.), Haydar Bulgak, Christoph Zenger (eds.)

Publisher: Springer Netherlands
Year: 1999
Tongue: English
Leaves: 363
Series: NATO Science Series 536
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc.
Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.

✦ Table of Contents

Front Matter....Pages i-xvi
Interval Arithmetic Tools for Range Approximation and Inclusion of Zeros....Pages 1-21
A New Concept of Construction of Adaptive Calculation Models for Hyperbolic Problems....Pages 23-64
Error Estimates in Linear Systems....Pages 65-74
Error Estimates in Padé Approximation....Pages 75-85
Error Estimates and Convergence Acceleration....Pages 87-94
Pseudoeigenvalues, Spectral Portrait of a Matrix and their Connections with Different Criteria of Stability....Pages 95-124
Error Control for Adaptive Sparse Grids....Pages 125-157
Orthogonal Matrix Decompositions in Systems and Control....Pages 159-175
Model Reduction of Large-Scale Systems Rational Krylov Versus Balancing Techniques....Pages 177-190
Adaptive Symplectic and Reversible Integrators....Pages 191-220
Domain Decomposition Methods for Compressible Flows....Pages 221-245
Error Control in Finite Element Computations....Pages 247-278
Verified Solution of Large Linear and Nonlinear Systems....Pages 279-298
The Accuracy of Numerical Models for Continuum Problems....Pages 299-323
Domain Decomposition Methods for Elliptic Partial Differential Equations....Pages 325-354

✦ Subjects

Computational Mathematics and Numerical Analysis;Numeric Computing;Algorithms;Appl.Mathematics/Computational Methods of Engineering;Mechanics

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