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Spherical Radial Basis Functions, Theory and Applications

  • Book
  • © 2015


  • 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:

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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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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Table of contents (6 chapters)


“The aim of the authors is to present enough practical and theoretical details to enable the reader to apply SBFs to solve real-world problems or to pursue theoretical investigations. … The book is clearly written and largely self-contained, and technical details are explained in an understandable way. It contains an interesting historical survey and many literature hints.” (Ilona Iglewska-Nowak, Mathematical Reviews, February, 2017)

Authors and Affiliations

  • School of Economics, Mathematics and Statistics, Birkbeck, University of London, London, United Kingdom

    Simon Hubbert

  • School of Mathematics, The University of New South Wales, Sydney, Australia

    Quôc Thông Lê Gia

  • MathWorks, Cambridge, United Kingdom

    Tanya M. Morton

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