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.
Author(s): Armin Iske, Jeremy Levesley
Edition: 1
Year: 2006
Language: English
Pages: 388
Contents......Page 7
Part I: Imaging and Data Mining......Page 14
Ranking as Function Approximation......Page 15
Two Algorithms for Approximation in Highly Complicated Planar Domains......Page 31
Computational Intelligence in Clustering Algorithms, With Applications......Page 43
Energy-Based Image Simplification with Nonlocal Data and Smoothness Terms......Page 63
Multiscale Voice Morphing Using Radial Basis Function Analysis......Page 73
Associating Families of Curves Using Feature Extraction and Cluster Analysis......Page 82
Part II: Numerical Simulation......Page 92
Particle Flow Simulation by Using Polyharmonic Splines......Page 93
Enhancing SPH using Moving Least-Squares and Radial Basis Functions......Page 113
Stepwise Calculation of the Basin of Attraction in Dynamical Systems Using Radial Basis Functions......Page 123
Integro-Differential Equation Models and Numerical Methods for Cell Motility and Alignment......Page 133
Spectral Galerkin Method Applied to Some Problems in Elasticity......Page 145
Part III: Statistical Approximation Methods......Page 155
Bayesian Field Theory Applied to Scattered Data Interpolation and Inverse Problems......Page 156
Algorithms for Structured Gauss-Markov Regression......Page 176
Uncertainty Evaluation in Reservoir Forecasting by Bayes Linear Methodology......Page 195
Part IV: Data Fitting and Modelling......Page 205
Integral Interpolation......Page 206
Shape Control in Powell-Sabin Quasi-Interpolation......Page 226
Approximation with Asymptotic Polynomials......Page 247
Spline Approximation Using Knot Density Functions......Page 255
Neutral Data Fitting by Lines and Planes......Page 265
Approximation on an Infinite Range to Ordinary Differential Equations Solutions by a Function of a Radial Basis Function......Page 275
Weighted Integrals of Polynomial Splines......Page 285
Part V: Differential and Integral Equations......Page 291
On Sequential Estimators for Affine Stochastic Delay Differential Equations......Page 292
Scalar Periodic Complex Delay Differential Equations: Small Solutions and their Detection......Page 302
Using Approximations to Lyapunov Exponents to Predict Changes in Dynamical Behaviour in Numerical Solutions to Stochastic Delay Differential Equations......Page 313
Superconvergence of Quadratic Spline Collocation for Volterra Integral Equations......Page 323
Part VI: Special Functions and Approximation on Manifolds......Page 332
Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions......Page 333
Strictly Positive Definite Functions on Generalized Motion Groups......Page 351
Energy Estimates and the Weyl Criterion on Compact Homogeneous Manifolds......Page 360
Minimal Discrete Energy Problems and Numerical Integration on Compact Sets in Euclidean Spaces......Page 369
Numerical Quadrature of Highly Oscillatory Integrals Using Derivatives......Page 378
F......Page 386
R......Page 387
Z......Page 388
