This book collects up-to-date papers from world experts in a broad variety of relevant applications of approximation theory, including dynamical systems, multiscale modelling of fluid flow, metrology, and geometric modelling to mention a few. The 14 papers in this volume document modern trends in approximation through recent theoretical developments, important computational aspects and multidisciplinary applications. The book is arranged in seven invited surveys, followed by seven contributed research papers. The surveys of the first seven chapters are addressing the following relevant topics: emergent behaviour in large electrical networks, algorithms for multivariate piecewise constant approximation, anisotropic triangulation methods in adaptive image approximation, form assessment in coordinate metrology, discontinuous Galerkin methods for linear problems, a numerical analyst's view of the lattice Boltzmann method, approximation of probability measures on manifolds. Moreover, the diverse contributed papers of the remaining seven chapters reflect recent developments in approximation theory, approximation practice and their applications. Graduate students who wish to discover the state of the art in a number of important directions of approximation algorithms will find this a valuable volume. Established researchers from statisticians through to fluid modellers will find interesting new approaches to solving familiar but challenging problems. This book grew out of the sixth in the conference series on "Algorithms for Approximation", which took place from 31st August to September 4th 2009 in Ambleside in the Lake District of the United Kingdom.
Author(s): Darryl P. Almond, Chris J. Budd, Nick J. McCullen (auth.), Emmanuil H Georgoulis, Armin Iske, Jeremy Levesley (eds.)
Series: Springer Proceedings in Mathematics 3
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 310
Tags: Approximations and Expansions; Algorithms; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Applications of Mathematics; Numerical Analysis
Front Matter....Pages i-x
Front Matter....Pages 11-11
Emergent Behaviour in Large Electrical Networks....Pages 3-26
Algorithms and Error Bounds for Multivariate Piecewise Constant Approximation....Pages 27-45
Anisotropic Triangulation Methods in Adaptive Image Approximation....Pages 47-68
Form Assessment in Coordinate Metrology....Pages 69-90
Discontinuous Galerkin Methods for Linear Problems: An Introduction....Pages 91-126
A Numerical Analyst’s View of the Lattice Boltzmann Method....Pages 127-150
Approximating Probability Measures on Manifolds via Radial Basis Functions....Pages 151-180
Front Matter....Pages 181-181
Modelling Clinical Decay Data Using Exponential Functions....Pages 183-203
Towards Calculating the Basin of Attraction of Non-Smooth Dynamical Systems Using Radial Basis Functions....Pages 205-225
Stabilizing Lattice Boltzmann Simulation of Fluid Flow past a Circular Cylinder with Ehrenfests’ Limiter....Pages 227-239
Fast and Stable Interpolation of Well Data Using the Norm Function....Pages 241-253
Algorithms and Literate Programs for Weighted Low-Rank Approximation with Missing Data....Pages 255-273
On Bivariate Interpolatory Mask Symbols, Subdivision and Refinable Functions....Pages 275-292
Model and Feature Selection in Metrology Data Approximation....Pages 293-307
