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Author : Stephen Hales
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (594 download)
Download or read book Approximation by Translates of a Radial Basis Function written by Stephen Hales and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin D. Buhmann
Publisher : Cambridge University Press
ISBN 13 : 1139435248
Total Pages : 271 pages
Book Rating : 4.1/5 (394 download)
Download or read book Radial Basis Functions written by Martin D. Buhmann and published by Cambridge University Press. This book was released on 2003-07-03 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence
Author :
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (227 download)
Download or read book Radial Basis Function Approximation: From Gridded Centers to Scattered Centers written by and published by . This book was released on 1993 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper studies L-infinity (IR d)-norm approximations from a space spanned by a discrete set of translates of a basis function theta. Attention here is restricted to functions theta whose Fourier transform is smooth on IRd/ 0, and has a singularity at the origin. Examples of such basis functions are the thin-plate splines and the multiquadrics, as well as other types of radial basis functions that are employed in Approximation Theory. The above approximation problem is well-understood in case the set of points used for translating theta forms a lattice in IR d, and many optimal and quasi-optimal approximation schemes can already be found in the literature. In contrast, only few, mostly specific, results are known for a set of scattered points. The main objective of this paper is to provide a general tool for extending approximation schemes that use integer translates of a basis function to the non-uniform case. We introduce a single, relatively simple, conversion method that preserves the approximation orders provided by a large number of schemes presently in the literature (more precisely, to almost all stationary schemes). In anticipation of future introduction of new schemes for uniform grids, an effort is made to impose only a few mild conditions on the function theta, which still allow for a unified error analysis to hold. In the course of the discussion here, the recent results of BuDL on scattered center approximation are reproduced and improved upon.
Author :
Publisher :
ISBN 13 : 9788416464326
Total Pages : 199 pages
Book Rating : 4.4/5 (643 download)
Download or read book Interpolation and Approximation by Delsarte Translates of Radial Basis Functions written by and published by . This book was released on 2015 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (227 download)
Download or read book Radial Base Functions: Lp-approximation Orders with Scattered Centres written by and published by . This book was released on 1994 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we generalize several results on uniform approximation orders with radial basis functions in (Buhmann, Dyn and Levin, 1993) and (Dyn and Ron, 1993) to Lp-approximation orders. These results apply, in particular, to approximates from spaces spanned by translates of radial basis functions by scattered centers. Examples to which our results apply include quasi- interpolation and least-squares approximation from radial function spaces.
Author : Gregory E. Fasshauer
Publisher : World Scientific
ISBN 13 : 981270633X
Total Pages : 520 pages
Book Rating : 4.8/5 (127 download)
Download or read book Meshfree Approximation Methods with MATLAB written by Gregory E. Fasshauer and published by World Scientific. This book was released on 2007 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.
Author : Martin Dietrich Buhmann
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (16 download)
Download or read book On the Density of Radial Function Spaces and Stability of Radial Function Approximations written by Martin Dietrich Buhmann and published by . This book was released on 1990 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give sufficient conditions on a radial basis function and study the location of sample points in R^s that imply that the space spanned by translates of the radial function along these sample points is dense in the space of continuous functions on a compact set. From this, we derive that these radial functions do not satisfy a stability estimate in the uniform norm. On the other hand, we also give a class of radial functions for which such an estimate holds.
Author : M. D. Buhmann
Publisher : Cambridge University Press
ISBN 13 : 9780521581905
Total Pages : 238 pages
Book Rating : 4.5/5 (819 download)
Download or read book Approximation Theory and Optimization written by M. D. Buhmann and published by Cambridge University Press. This book was released on 1997-11-13 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Michael Powell is one of the world's foremost figures in numerical analysis. This volume, first published in 1997, is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell's own achievements, focuses on innovative work in optimisation and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys. They have all been reviewed and edited to form a coherent volume for this important discipline within mathematics, with highly relevant applications throughout science and engineering.
Author : Thomas Hangelbroek
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (89 download)
Download or read book Approximation by Scattered Translates of the Fundamental Solution of the Biharmonic Equations on Bounded Domains written by Thomas Hangelbroek and published by . This book was released on 2007 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Holger Wendland
Publisher : Cambridge University Press
ISBN 13 : 9781139456654
Total Pages : 346 pages
Book Rating : 4.4/5 (566 download)
Download or read book Scattered Data Approximation written by Holger Wendland and published by Cambridge University Press. This book was released on 2004-12-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations.
Author : Elliott Ward Cheney
Publisher : American Mathematical Soc.
ISBN 13 : 0821847988
Total Pages : 379 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Course in Approximation Theory written by Elliott Ward Cheney and published by American Mathematical Soc.. This book was released on 2009-01-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.
Author : Jungho Yoon
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.:/5 (89 download)
Download or read book Approximation to Scattered Data by Radial Basis Function written by Jungho Yoon and published by . This book was released on 1998 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George Anastassiou
Publisher : CRC Press
ISBN 13 : 9780824787080
Total Pages : 558 pages
Book Rating : 4.7/5 (87 download)
Download or read book Approximation Theory written by George Anastassiou and published by CRC Press. This book was released on 1992-04-24 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the March 1991 annual conference of the Southeastern Approximation Theorists, in Memphis, Tenn. The 34 papers discuss topics of interest to graduate and professional numerical analysts, applied and industrial mathematicians, engineers, and other scientists such as splines
Author : Kurt Jetter
Publisher : World Scientific
ISBN 13 : 9814602523
Total Pages : 349 pages
Book Rating : 4.8/5 (146 download)
Download or read book Multivariate Approximation : From Cagd To Wavelets - Proceedings Of The International Workshop written by Kurt Jetter and published by World Scientific. This book was released on 1993-11-30 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Fast Algorithms for Simultaneous Polynomial Approximation (G Baszenski & M Tasche)α-Spline of Smoothing for Correlated Errors in Dimension Two (M Bozzini & L Lenarduzzi)New Developments in the Theory of Radial Basis Function Interpolation (M D Buhmann)Realization of Neural Networks with One Hidden Layer (C K Chui & X Li)A General Method for Constrained Curves with Boundary Conditions (P Costantini)Sign-Regular and Totally Positive Matrices: An Algorithmic Approach (M Gasca & J M Peña)Some Results on Blossoming and Multivariate B-Splines (R Gormaz & P-J Laurent)Riesz Bounds in Scattered Data Interpolation and L2-Approximation (K Jetter)On Multivariate Hermite Polynomial Interpolation (A Le Méhauté)Quantitative Approximation Results for Sigma-Pi-Type Neural Network Operators (B Lenze)Local Interpolation Schemes — From Curves to Surfaces (D Levin)Some Results on Approximation by Smoothing Dm-Splines (M C L de Silanes) Readership: Applied mathematicians.
Author : Charles K Chui
Publisher : World Scientific
ISBN 13 : 9814549061
Total Pages : 606 pages
Book Rating : 4.8/5 (145 download)
Download or read book Approximation Theory Viii - Volume 1: Approximation And Interpolation written by Charles K Chui and published by World Scientific. This book was released on 1995-11-07 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.
Author : Wen Chen
Publisher : Springer Science & Business Media
ISBN 13 : 3642395724
Total Pages : 98 pages
Book Rating : 4.6/5 (423 download)
Download or read book Recent Advances in Radial Basis Function Collocation Methods written by Wen Chen and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s problems. This book is intended to meet this need. Prof. Wen Chen and Dr. Zhuo-Jia Fu work at Hohai University. Prof. C.S. Chen works at the University of Southern Mississippi.
Author : Charles K. Chui
Publisher : World Scientific
ISBN 13 : 9814532592
Total Pages : 606 pages
Book Rating : 4.8/5 (145 download)
Download or read book Approximation Theory VIII written by Charles K. Chui and published by World Scientific. This book was released on 1995 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.
