Overview
- A customised review of spherical mathematics from functional analysis and differential geometry
- Studies technical error analysis of the SBF method in a friendly, readable style
- Both practical and theoretical issues are covered
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (6 chapters)
Keywords
About this book
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.
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Bibliographic Information
Book Title: Spherical Radial Basis Functions, Theory and Applications
Authors: Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-17939-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2015
Softcover ISBN: 978-3-319-17938-4Published: 27 May 2015
eBook ISBN: 978-3-319-17939-1Published: 13 May 2015
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 143
Number of Illustrations: 4 b/w illustrations, 3 illustrations in colour
Topics: Approximations and Expansions, Partial Differential Equations, Numerical Analysis, Global Analysis and Analysis on Manifolds, Geophysics/Geodesy