Radial Basis Functions
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Radial Basis Functions
Author: Martin D. Buhmann
language: en
Publisher: Cambridge University Press
Release Date: 2003-07-03
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
Radial Basis Function Networks 2
The Radial Basis Function (RBF) network has gained in popularity in recent years. This is due to its desirable properties in classification and functional approximation applications, accompanied by training that is more rapid than that of many other neural-network techniques. RBF network research has focused on enhanced training algorithms and variations on the basic architecture to improve the performance of the network. In addition, the RBF network is proving to be a valuable tool in a diverse range of applications areas, for example, robotics, biomedical engineering, and the financial sector. The two-title series Theory and Applications of Radial Basis Function Networks provides a comprehensive survey of recent RBF network research. This volume, New Advances in Design, contains a wide range of applications in the laboratory and case-studies describing current use. The sister volume to this one, Recent Developments in Theory and Applications, covers advances in training algorithms, variations on the architecture and function of the basis neurons, and hybrid paradigms. The combination of the two volumes will prove extremely useful to practitioners in the field, engineers, researchers, students and technically accomplished managers.
A Primer on Radial Basis Functions with Applications to the Geosciences
?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.