Approximation To Scattered Data By Radial Basis Function

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Scattered Data Approximation

Author : Holger Wendland
Publisher : Cambridge University Press
ISBN 13 : 9781139456654
Total Pages : 346 pages
Book Rating : 4.4/5 (566 download)

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Book Synopsis Scattered Data Approximation by : Holger Wendland

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.

Approximation to Scattered Data by Radial Basis Function

Author : Jungho Yoon
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Approximation to Scattered Data by Radial Basis Function by : Jungho Yoon

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:

Meshfree Approximation Methods with MATLAB

Author : Gregory E. Fasshauer
Publisher : World Scientific
ISBN 13 : 981270633X
Total Pages : 520 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Meshfree Approximation Methods with MATLAB by : Gregory E. Fasshauer

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.

Topics in Multivariate Approximation

Author : C. K. Chui
Publisher : Elsevier
ISBN 13 : 1483271005
Total Pages : 346 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Topics in Multivariate Approximation by : C. K. Chui

Download or read book Topics in Multivariate Approximation written by C. K. Chui and published by Elsevier. This book was released on 2014-05-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

Radial Basis Functions

Author : Martin D. Buhmann
Publisher : Cambridge University Press
ISBN 13 : 1139435248
Total Pages : 271 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Radial Basis Functions by : Martin D. Buhmann

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

Multiresolution Methods in Scattered Data Modelling

Author : Armin Iske
Publisher : Springer Science & Business Media
ISBN 13 : 3642187544
Total Pages : 195 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Multiresolution Methods in Scattered Data Modelling by : Armin Iske

Download or read book Multiresolution Methods in Scattered Data Modelling written by Armin Iske and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This application-oriented work concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena. To this end, various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. The resulting multiresolution methods include thinning algorithms, multi levelapproximation schemes, and meshfree discretizations for transport equa tions. The utility of the proposed computational methods is supported by their wide range of applications, such as image compression, hierarchical sur face visualization, and multiscale flow simulation. Special emphasis is placed on comparisons between the various numerical algorithms developed in this work and comparable state-of-the-art methods. To this end, extensive numerical examples, mainly arising from real-world applications, are provided. This research monograph is arranged in six chapters: 1. Introduction; 2. Algorithms and Data Structures; 3. Radial Basis Functions; 4. Thinning Algorithms; 5. Multilevel Approximation Schemes; 6. Meshfree Methods for Transport Equations. Chapter 1 provides a preliminary discussion on basic concepts, tools and principles of multiresolution methods, scattered data modelling, multilevel methods and adaptive irregular sampling. Relevant algorithms and data structures, such as triangulation methods, heaps, and quadtrees, are then introduced in Chapter 2.

Recent Advances in Radial Basis Function Collocation Methods

Author : Wen Chen
Publisher : Springer Science & Business Media
ISBN 13 : 3642395724
Total Pages : 98 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Recent Advances in Radial Basis Function Collocation Methods by : Wen Chen

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.

A Primer on Radial Basis Functions with Applications to the Geosciences

Author : Bengt Fornberg
Publisher : SIAM
ISBN 13 : 1611974046
Total Pages : 226 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis A Primer on Radial Basis Functions with Applications to the Geosciences by : Bengt Fornberg

Download or read book A Primer on Radial Basis Functions with Applications to the Geosciences written by Bengt Fornberg and published by SIAM. This book was released on 2015-09-30 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work. The authors trace the algorithmic evolution of RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others. This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.

New Developments in Approximation Theory

Author : Manfred W. Müller
Publisher : Springer
ISBN 13 : 3034886969
Total Pages : 337 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis New Developments in Approximation Theory by : Manfred W. Müller

Download or read book New Developments in Approximation Theory written by Manfred W. Müller and published by Springer. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers by international contributors describing new developments in the fields of univariate and multivariate approximation theory. This research has applications in areas such as computer-aided geometric design, as applied in engineering and medical technology (e.g. computerized tomography).

Kernel-based Approximation Methods Using Matlab

Author : Gregory E Fasshauer
Publisher : World Scientific Publishing Company
ISBN 13 : 9814630152
Total Pages : 537 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Kernel-based Approximation Methods Using Matlab by : Gregory E Fasshauer

Download or read book Kernel-based Approximation Methods Using Matlab written by Gregory E Fasshauer and published by World Scientific Publishing Company. This book was released on 2015-07-30 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Approximation Theory XV

Author : Gregory E. Fasshauer
Publisher :
ISBN 13 : 9783319599137
Total Pages : 398 pages
Book Rating : 4.5/5 (991 download)

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Book Synopsis Approximation Theory XV by : Gregory E. Fasshauer

Download or read book Approximation Theory XV written by Gregory E. Fasshauer and published by . This book was released on 2017 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Adaptive High-order Methods in Computational Fluid Dynamics

Author : Z. J. Wang
Publisher : World Scientific
ISBN 13 : 9814313181
Total Pages : 471 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Adaptive High-order Methods in Computational Fluid Dynamics by : Z. J. Wang

Download or read book Adaptive High-order Methods in Computational Fluid Dynamics written by Z. J. Wang and published by World Scientific. This book was released on 2011 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.

Advances in Computational Mathematics

Author : Zhongying Chen
Publisher : CRC Press
ISBN 13 : 100094817X
Total Pages : 636 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Advances in Computational Mathematics by : Zhongying Chen

Download or read book Advances in Computational Mathematics written by Zhongying Chen and published by CRC Press. This book was released on 2023-08-25 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the refereed proceedings of the Guangzhou International Symposium on Computational Mathematics, held at the Zhongshan University, People's Republic of China. Nearly 90 international mathematicians examine numerical optimization methods, wavelet analysis, computational approximation, numerical solutions of differential and integral equations, numerical linear algebra, inverse and ill-posed problems, geometric modelling, and signal and image processing and their applications.

Algorithms for Approximation

Author : J. C. Mason
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 732 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Algorithms for Approximation by : J. C. Mason

Download or read book Algorithms for Approximation written by J. C. Mason and published by Oxford University Press, USA. This book was released on 1987 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "approximation" here refers to the approximation of functions and data by simple functions. Emphasizing the development of useful algorithms and practical applications in defense and industry, the papers cover topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours. Includes a substantial catalog of existing algorithms. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Refined Error Estimates for Matrix-valued Radial Basis Functions

Author : Edward J. Fuselier
Publisher :
ISBN 13 :
Total Pages : 79 pages
Book Rating : 4.:/5 (463 download)

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Book Synopsis Refined Error Estimates for Matrix-valued Radial Basis Functions by : Edward J. Fuselier

Download or read book Refined Error Estimates for Matrix-valued Radial Basis Functions written by Edward J. Fuselier and published by . This book was released on 2006 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: Radial basis functions (RBFs) are probably best known for their applications to scattered data problems. Until the 1990s, RBF theory only involved functions that were scalar-valued. Matrix-valued RBFs were subsequently introduced by Narcowich and Ward in 1994, when they constructed divergence-free vector-valued functions that interpolate data at scattered points. In 2002, Lowitzsch gave the first error estimates for divergence-free interpolants. However, these estimates are only valid when the target function resides in the native space of the RBF. In this paper we develop Sobolev-type error estimates for cases where the target function is less smooth than functions in the native space. In the process of doing this, we give an alternate characterization of the native space, derive improved stability estimates for the interpolation matrix, and give divergence-free interpolation and approximation results for band-limited functions. Furthermore, we introduce a new class of matrix-valued RBFs that can be used to produce curl-free interpolants.

From Statistics to Neural Networks

Author : Vladimir Cherkassky
Publisher : Springer Science & Business Media
ISBN 13 : 3642791190
Total Pages : 414 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis From Statistics to Neural Networks by : Vladimir Cherkassky

Download or read book From Statistics to Neural Networks written by Vladimir Cherkassky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute From Statistics to Neural Networks, Theory and Pattern Recognition Applications took place in Les Arcs, Bourg Saint Maurice, France, from June 21 through July 2, 1993. The meeting brought to gether over 100 participants (including 19 invited lecturers) from 20 countries. The invited lecturers whose contributions appear in this volume are: L. Almeida (INESC, Portugal), G. Carpenter (Boston, USA), V. Cherkassky (Minnesota, USA), F. Fogelman Soulie (LRI, France), W. Freeman (Berkeley, USA), J. Friedman (Stanford, USA), F. Girosi (MIT, USA and IRST, Italy), S. Grossberg (Boston, USA), T. Hastie (AT&T, USA), J. Kittler (Surrey, UK), R. Lippmann (MIT Lincoln Lab, USA), J. Moody (OGI, USA), G. Palm (U1m, Germany), B. Ripley (Oxford, UK), R. Tibshirani (Toronto, Canada), H. Wechsler (GMU, USA), C. Wellekens (Eurecom, France) and H. White (San Diego, USA). The ASI consisted of lectures overviewing major aspects of statistical and neural network learning, their links to biological learning and non-linear dynamics (chaos), and real-life examples of pattern recognition applications. As a result of lively interactions between the participants, the following topics emerged as major themes of the meeting: (1) Unified framework for the study of Predictive Learning in Statistics and Artificial Neural Networks (ANNs); (2) Differences and similarities between statistical and ANN methods for non parametric estimation from examples (learning); (3) Fundamental connections between artificial learning systems and biological learning systems.

Geometric Modeling

Author : Hans Hagen
Publisher : Springer Science & Business Media
ISBN 13 : 3642764045
Total Pages : 291 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Geometric Modeling by : Hans Hagen

Download or read book Geometric Modeling written by Hans Hagen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.