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Methods of Shape-Preserving Spline Approximation
Boris I. Kvasov «Methods of Shape-Preserving Spline Approximation»
World Scientific Publishing Company | ISBN 9810240104 | September 2000 | djvu (600 dpi scan) | 418 Pages | 17.5 MB
This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces.
Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
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Algorithms for Approximation: Proceedings of the 5th International Conference, Chester, July 2005
Armin Iske, Jeremy Levesley, «Algorithms for Approximation:
Proceedings of the 5th International Conference, Chester, July 2005»
Springer | ISBN 3540332839 | December 2006 | PDF | 10.9 Mb | 389 pages
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.
Written for:
Graduate students and researchers in Approximation Theory, Numerical Analysis, Multiresolution, Geometric Modeling
Table of contents
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 Asymptotic Polynomials –
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
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