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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.
List of contents
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.
About the author
Prof. Dr. Christoph Zenger ist Ordinarius für Ingenieuranwendungen in der Informatik und numerische Programmierung am Institut für Informatik der TU München.
Summary
Proceedings of the NATO Advanced Study Institute, Antalya, Turkey, August 9-21, 1998
