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.
Part I Imaging and Data Mining Ranking as Function Approximation - Christopher J.C. Burges Two Algorithms for Approximation in Highly Complicated Planar Domains - Nira Dyn, Roman Computational Intelligence in Clustering Algorithms, With Applications - Rui Xu, Donald Wunsch II Energy-Based Image Simplification with Nonlocal Data and Smoothness Terms – Stephan Didas, Pavel Mr´azek, Joachim Weickert Multiscale Voice Morphing Using Radial Basis Function Analysis - Christina Orphanidou, Irene M. Moroz, Stephen J. Roberts Associating Families of Curves Using Feature Extraction and Cluster Analysis - Jane L. Terry, Andrew Crampton, Chris J. Talbot Part II Numerical Simulation Particle Flow Simulation by Using Polyharmonic Splines - Armin Iske Enhancing SPH using Moving Least-Squares and Radial Basis Functions - Robert Brownlee, Paul Houston, Jeremy Levesley, Stephan Rosswog Stepwise Calculation of the Basin of Attraction in Dynamical Systems Using Radial Basis Functions - Peter Giesl Integro-Differential Equation Models and Numerical Methods for Cell Motility and Alignment - Athena Makroglou Spectral Galerkin Method Applied to Some Problems in Elasticity - Chris J. Talbot Part III Statistical Approximation Methods Bayesian Field Theory Applied to Scattered Data Interpolation and Inverse Problems -Chris L. Farmer Algorithms for Structured Gauss-Markov Regression - Alistair B. Forbes Uncertainty Evaluation in Reservoir Forecasting by Bayes Linear Methodology - Daniel Busby, Chris L. Farmer, Armin Iske Part IV Data Fitting and Modelling Integral Interpolation - Rick K. Beatson, Michael K. Langton Shape Control in Powell-Sabin Quasi-Interpolation - Carla Manni Approximation with AsymptoticPolynomials – Philip Cooper, Alistair B. Forbes, John C. Mason Spline Approximation Using Knot Density Functions - Andrew Crampton, Alistair B. Forbes Neutral Data Fitting by Lines and Plane - Tim Goodman, Chris Tofallis Approximation on an Infinite Range to Ordinary Differential Equations Solutions by a Function of a Radial Basis Function - Damian P. Jenkinson, John C. Mason Weighted Integrals of Polynomial Splines - Mladen Rogina Part V Differential and Integral Equations On Sequential Estimators for an Affine Stochastic Delay Differential Equations - Uwe Küchler, Vyacheslav Vasiliev Scalar Periodic Complex Delay Differential Equations: Small Solutions and their Detection - Neville J. Ford, Patricia M. Lumb Using Approximations to Lyapunov Exponents to Predict Changes in Dynamical Behaviour in Numerical Solutions to Stochastic Delay Differential Equations – Neville J. Ford, Stewart J. Norton Superconvergence of Quadratic Spline Collocation for Volterra Integral Equations - Darja Saveljeva Part VI Special Functions and Approximation on Manifolds Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions - Ernst Joachim Weniger Strictly Positive Definite Functions on Generalized Motion Groups – Wolfgang zu Castell, Frank Filbir - Energy Estimates and the Weyl Criterion on Compact Homogeneous Manifolds - Steven B. Damelin, Jeremy Levesley, Xingping Sun Minimal Discrete Energy Problems and Numerical Integration on Compact Sets in Euclidean Spaces - Steven B. Damelin, Viktor Maymeskul Numerical Quadrature of Highly Oscillatory Integrals Using Derivatives - Sheehan Olver Index
