Error Control and Adaptivity in Scientific Computing

1999
ISBN: 978-0-7923-5808-4
Verlag: Springer Netherlands

Buch, Englisch, Band 536, 354 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1550 g

Reihe: Nato Science Series C:

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.

Zielgruppe

Research

Autoren/Hrsg.

Zenger, Christoph

Bulgak, Haydar

Fachgebiete

• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik EDV | Informatik Informatik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Interval Arithmetic Tools for Range Approximation and Inclusion of Zeros.- A New Concept of Construction of Adaptive Calculation Models for Hyperbolic Problems.- Error Estimates in Linear Systems.- Error Estimates in Padé Approximation.- Error Estimates and Convergence Acceleration.- Pseudoeigenvalues Spectral Portrait of a Matrix and their Connections with Different Criteria of Stability.- Error Control for Adaptive Sparse Grids.- Orthogonal Matrix Decompositions in Systems and Control.- Model Reduction of Large-Scale Systems, Rational Krylov versus Balancing Techniques.- Adaptive Symplectic and Reversible Integrators.- Domain Decomposition Methods for Compressible Flows.- Error Control in Finite Element Computations. An introduction to error estimation and mesh-size adaption.- Verified Solution of Large Linear and Nonlinear Systems.- The Accuracy of Numerical Models for Continuum Problems.- Domain Decomposition Methods for Elliptic Partial Differential Equations.