Spherical radial basis functions, theory and applications [electronic resource] / Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton.
Hubbert, Simon, author.; Gia, Quôc Thông Lê, author.; Morton, Tanya M., author.
2015
QA406
Available Online

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Title Spherical radial basis functions, theory and applications [electronic resource] / Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton.
Author Hubbert, Simon, author.
ISBN 9783319179391 electronic book
331917939X electronic book
9783319179384
DOI https://doi.org/10.1007/978-3-319-17939-1
Published Cham : Springer, [2015]
Language English
Description 1 online resource : color illustrations.
Item Number 10.1007/978-3-319-17939-1 doi
Call Number QA406
Dewey Decimal Classification 515/.53
Summary 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.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (viewed May 18, 2015).
Added Author Gia, Quôc Thông Lê, author.
Morton, Tanya M., author.
Series SpringerBriefs in mathematics.
Available in Other Form Print version: 9783319179384
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Motivation and Background Functional Analysis
The Spherical Basis Function Method
Error Bounds via Duchon's Technique
Radial Basis Functions for the Sphere
Fast Iterative Solvers for PDEs on Spheres
Parabolic PDEs on Spheres.

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