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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.

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Part I INVITED SURVEYS: Emergent Behaviour in Large Electrical Networks by D. P. Almond, C.J. Budd, N.J. McCullen.- Algorithms and Error Bounds for Multivariate Piecewise Constant Approximation by O. Davydov.- Anisotropic Triangulation Methods in Adaptive Image Approximation by L. Demaret, A. Iske.- Form Assessment in Coordinate Metrology by A.B. Forbes and H.D.Minh.- Discontinuous Galerkin Methods for Linear Problems: An Introduction by E. H. Georgoulis.- A Numerical Analyst´s View of the Lattice Boltzmann Method by A. G. Gorban, J. Levesley, D. Packwood.- Approximating Probability Measures on Manifolds via Radial Basis Functions by J. Levesley, X. Sun.- Part II CONTRIBUTED RESEARCH PAPERS: Modelling Clinical Decay Data Using Exponential Functions by M.G. Cox.- Towards Calculating the Basin of Attraction of Non-Smooth Dynamical Systems Using Radial Basis Functions by P. Giesl.- Stabilizing Lattice Boltzmann Simulation of Fluid Flow past a Circular Cylinder with Ehrenfests´ Limiter by T.S. Khan, J. Levesley.- Fast and Stable Interpolation of Well Data Using the Norm Function by B. Li, J. Levesley.- Algorithms and Literate Programs for Weighted Low-Rank Approximation with Missing Data by I. Markovsky.- On Bivariate Interpolatory Mask Symbols, Subdivision and Refinable Functions by A. F. Rabarison, J. de Villiers.- Model and Feature Selection in Metrology Data Approximation by X. Yang, A. B. Forbes.

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