Imaging and Data Mining -- Ranking as Function Approximation -- Two Algorithms for Approximation in Highly Complicated Planar Domains -- Computational Intelligence in Clustering Algorithms, With Applications -- Energy-Based Image Simplification with Nonlocal Data and Smoothness Terms -- Multiscale Voice Morphing Using Radial Basis Function Analysis -- Associating Families of Curves Using Feature Extraction and Cluster Analysis -- Numerical Simulation -- Particle Flow Simulation by Using Polyharmonic Splines -- Enhancing SPH using Moving Least-Squares and Radial Basis Functions -- Stepwise Calculation of the Basin of Attractionin Dynamical Systems Using Radial Basis Functions -- Integro-Differential Equation Models and Numerical Methods for Cell Motility and Alignment -- Spectral Galerkin Method Applied to Some Problems in Elasticity -- Statistical Approximation Methods -- Bayesian Field Theory Applied to Scattered Data Interpolation and Inverse Problems -- Algorithms for Structured Gauss-Markov Regression -- Uncertainty Evaluation in Reservoir Forecasting by Bayes Linear Methodology -- Data Fitting and Modelling -- Integral Interpolation -- Shape Control in Powell-Sabin Quasi-Interpolation -- Approximation with Asymptotic Polynomials -- Spline Approximation Using Knot Density Functions -- Neutral Data Fitting by Lines and Planes -- Approximation on an Infinite Range to Ordinary Differential Equations Solutions by a Function of a Radial Basis function -- Weighted Integrals of Polynomial Splines -- Differential and Integral Equations -- On Sequential Estimators for Affine Stochastic Delay Differential Equations -- Scalar Periodic Complex Delay Differential Equations: Small Solutions and their Detection -- Using Approximations to Lyapunov Exponents to Predict Changes in Dynamical Behaviour in Numerical Solutions to Stochastic Delay Differential Equations -- Superconvergence of Quadratic Spline Collocation for Volterra Integral Equations -- Special Functions and Approximation on Manifolds -- Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions -- Strictly Positive Definite Functions on Generalized Motion Groups -- Energy Estimates and the Weyl Criterion on Compact Homogeneous Manifolds -- Minimal Discrete Energy Problems and Numerical Integration on Compact Sets in Euclidean Spaces -- Numerical Quadrature of Highly Oscillatory Integrals Using Derivatives.

Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.