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Error Control and Adaptivity in Scientific Computing

  • Book
  • © 1999

Overview

Editors:
  1. Haydar Bulgak

    1. Research Center of Applied Mathematics, Selcuk University, Konya, Turkey

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    You can also search for this editor in PubMed   Google Scholar

  2. Christoph Zenger

    1. Institut für Informatik, Technische Universität München, München, Germany

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nato Science Series C: (ASIC, volume 536)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Interval Arithmetic Tools for Range Approximation and Inclusion of Zeros

    • G. Alefeld
    Pages 1-21

  3. A New Concept of Construction of Adaptive Calculation Models for Hyperbolic Problems

    • A. M. Blokhin
    Pages 23-64

  4. Error Estimates in Linear Systems

    • C. Brezinski
    Pages 65-74

  5. Error Estimates in Padé Approximation

    • C. Brezinski
    Pages 75-85

  6. Error Estimates and Convergence Acceleration

    • C. Brezinski
    Pages 87-94

  7. Pseudoeigenvalues, Spectral Portrait of a Matrix and their Connections with Different Criteria of Stability

    • H. Bulgak
    Pages 95-124

  8. Error Control for Adaptive Sparse Grids

    • Hans-Joachim Bungartz, Christoph Zenger
    Pages 125-157

  9. Orthogonal Matrix Decompositions in Systems and Control

    • P. M. Van Dooren
    Pages 159-175

  10. Model Reduction of Large-Scale Systems Rational Krylov Versus Balancing Techniques

    • K. A. Gallivan, E. Grimme, P. M. Van Dooren
    Pages 177-190

  11. Adaptive Symplectic and Reversible Integrators

    • B. Karasözen
    Pages 191-220

  12. Domain Decomposition Methods for Compressible Flows

    • Alfio Quarteroni, Alberto Valli
    Pages 221-245

  13. Error Control in Finite Element Computations

    • R. Rannacher
    Pages 247-278

  14. Verified Solution of Large Linear and Nonlinear Systems

    • Siegfried M. Rump
    Pages 279-298

  15. The Accuracy of Numerical Models for Continuum Problems

    • Stanly Steinberg
    Pages 299-323

  16. Domain Decomposition Methods for Elliptic Partial Differential Equations

    • Olof B. Widlund
    Pages 325-354
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Keywords

About this book

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.

Editors and Affiliations

  • Research Center of Applied Mathematics, Selcuk University, Konya, Turkey

    Haydar Bulgak

  • Institut für Informatik, Technische Universität München, München, Germany

    Christoph Zenger

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