Author : Martin D. Buhmann
Publisher : Cambridge University Press
Page : 271 pages
File Size : 22,14 MB
Release : 2003-07-03
Category : Mathematics
ISBN : 1139435248
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 : Marco Evangelos Biancolini
Publisher : Springer
Page : 366 pages
File Size : 18,85 MB
Release : 2018-03-29
Category : Computers
ISBN : 3319750119
This book presents the first “How To” guide to the use of radial basis functions (RBF). It provides a clear vision of their potential, an overview of ready-for-use computational tools and precise guidelines to implement new engineering applications of RBF. Radial basis functions (RBF) are a mathematical tool mature enough for useful engineering applications. Their mathematical foundation is well established and the tool has proven to be effective in many fields, as the mathematical framework can be adapted in several ways. A candidate application can be faced considering the features of RBF: multidimensional space (including 2D and 3D), numerous radial functions available, global and compact support, interpolation/regression. This great flexibility makes RBF attractive – and their great potential has only been partially discovered. This is because of the difficulty in taking a first step toward RBF as they are not commonly part of engineers’ cultural background, but also due to the numerical complexity of RBF problems that scales up very quickly with the number of RBF centers. Fast RBF algorithms are available to alleviate this and high-performance computing (HPC) can provide further aid. Nevertheless, a consolidated tradition in using RBF in engineering applications is still missing and the beginner can be confused by the literature, which in many cases is presented with language and symbolisms familiar to mathematicians but which can be cryptic for engineers. The book is divided in two main sections. The first covers the foundations of RBF, the tools available for their quick implementation and guidelines for facing new challenges; the second part is a collection of practical RBF applications in engineering, covering several topics, including response surface interpolation in n-dimensional spaces, mapping of magnetic loads, mapping of pressure loads, up-scaling of flow fields, stress/strain analysis by experimental displacement fields, implicit surfaces, mesh to cad deformation, mesh morphing for crack propagation in 3D, ice and snow accretion using computational fluid dynamics (CFD) data, shape optimization for external aerodynamics, and use of adjoint data for surface sculpting. For each application, the complete path is clearly and consistently exposed using the systematic approach defined in the first section.
Author : Wen Chen
Publisher : Springer Science & Business Media
Page : 98 pages
File Size : 24,8 MB
Release : 2013-11-09
Category : Technology & Engineering
ISBN : 3642395724
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 : N. Sundararajan
Publisher : World Scientific
Page : 236 pages
File Size : 11,78 MB
Release : 1999
Category : Science
ISBN : 9789810237714
A review of radial basis founction (RBF) neural networks. A novel sequential learning algorithm for minimal resource allocation neural networks (MRAN). MRAN for function approximation & pattern classification problems; MRAN for nonlinear dynamic systems; MRAN for communication channel equalization; Concluding remarks; A outline source code for MRAN in MATLAB; Bibliography; Index.
Author : Simon Hubbert
Publisher : Springer
Page : 150 pages
File Size : 16,14 MB
Release : 2015-05-13
Category : Mathematics
ISBN : 331917939X
This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics.
Author : Peter Giesl
Publisher : Springer
Page : 175 pages
File Size : 12,95 MB
Release : 2007-04-11
Category : Mathematics
ISBN : 3540699090
The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.
Author : Gregory E. Fasshauer
Publisher : World Scientific
Page : 520 pages
File Size : 43,4 MB
Release : 2007
Category : Technology & Engineering
ISBN : 981270633X
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 : Manfred W. Müller
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 24,1 MB
Release : 1999
Category : Mathematics
ISBN : 9783764361433
This book contains refereed papers which were presented at the Second International Dortmund Meeting on Approximation Theory (IDoMAT '98) at Haus Bommerholz, the conference center of Dortmund University, during the week of February 23-27, 1998. At this conference 50 researchers and specialists from Bulgaria, China, France, Great Britain, Hungary, Israel, Italy, Romania, South Africa and Germany participated and described new developments in the fields of univariate and multivariate approximation theory. The papers cover topics such as radial basis functions, bivariate spline interpolation, subdivision algorithms, multilevel interpolation, multivariate triangular Bernstein bases, Padè approximation, comonotone polynomial approximation, weighted and unweighted polynomial approximation, adaptive approximation, approximation operators of binomial type, quasi-interpolants, generalized convexity and Peano kernel techniques.This research has applications in areas such as computer-aided geometric design, as applied in engineering and medical technology (e.g. computerized tomography).
Author : Sandeep Kumar Satapathy
Publisher : Academic Press
Page : 136 pages
File Size : 22,22 MB
Release : 2019-02-10
Category : Science
ISBN : 0128174277
EEG Brain Signal Classification for Epileptic Seizure Disorder Detection provides the knowledge necessary to classify EEG brain signals to detect epileptic seizures using machine learning techniques. Chapters present an overview of machine learning techniques and the tools available, discuss previous studies, present empirical studies on the performance of the NN and SVM classifiers, discuss RBF neural networks trained with an improved PSO algorithm for epilepsy identification, and cover ABC algorithm optimized RBFNN for classification of EEG signal. Final chapter present future developments in the field. This book is a valuable source for bioinformaticians, medical doctors and other members of the biomedical field who need the most recent and promising automated techniques for EEG classification. - Explores machine learning techniques that have been modified and validated for the purpose of EEG signal classification using Discrete Wavelet Transform for the identification of epileptic seizures - Encompasses machine learning techniques, providing an easily understood resource for both non-specialized readers and biomedical researchers - Provides a number of experimental analyses, with their results discussed and appropriately validated
Author : Holger Wendland
Publisher : Cambridge University Press
Page : 346 pages
File Size : 41,32 MB
Release : 2004-12-13
Category : Mathematics
ISBN : 9781139456654
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.
