EAN: 9783319179384

SPRINGERBRIEFS IN MATHEMATICS SPHERICAL RADIA...

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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