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Radial Basis Functions

Theory and Implementations

Radial Basis Functions by Martin D. Buhmann
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In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the limitations of other methods, such as least squares, polynomial interpolation or wavelet-based, become apparent. 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. A comprehensive bibliography rounds off what will prove a very valuable work.
Cambridge University Press; July 2003
271 pages; ISBN 9780511036019
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Title: Radial Basis Functions
Author: Martin D. Buhmann
 
ISBNs
0511036019
9780511036019
9780521633383