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Spherical Radial Basis Functions, Theory and Applications

  • Simon Hubbert
  • Quôc Thông Lê Gia
  • Tanya M. Morton

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
    Pages 1-28
  3. Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
    Pages 29-58
  4. Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
    Pages 59-83
  5. Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
    Pages 85-95
  6. Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
    Pages 97-119
  7. Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
    Pages 121-138
  8. Back Matter
    Pages 139-143

About this book

Introduction

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.

Keywords

Approximation Theory Approximation on Spheres Error Estimates Multivariate Interpolation Radial Basis Functions Spherical Harmonics

Authors and affiliations

  • Simon Hubbert
    • 1
  • Quôc Thông Lê Gia
    • 2
  • Tanya M. Morton
    • 3
  1. 1.School of Economics, Mathematics and StatisticsBirkbeck, University of LondonLondonUnited Kingdom
  2. 2.School of MathematicsThe University of New South WalesSydneyAustralia
  3. 3.MathWorksCambridgeUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-17939-1
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-17938-4
  • Online ISBN 978-3-319-17939-1
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site