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150601  eng 
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a 9783319179391

100 
1 

a Hubbert, Simon

245 
0 
0 
a Spherical Radial Basis Functions, Theory and Applications
h Elektronische Ressource
c by Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton

250 


a 1st ed. 2015

260 


a Cham
b Springer International Publishing
c 2015, 2015

300 


a X, 143 p. 7 illus., 3 illus. in color
b online resource

505 
0 

a 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

653 


a Geophysics

653 


a Numerical Analysis

653 


a Approximations and Expansions

653 


a Numerical analysis

653 


a Manifolds (Mathematics)

653 


a Approximation theory

653 


a Differential Equations

653 


a Global analysis (Mathematics)

653 


a Global Analysis and Analysis on Manifolds

653 


a Differential equations

700 
1 

a Le Gia, Quôc Thông
e [author]

700 
1 

a Morton, Tanya M.
e [author]

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a SpringerBriefs in Mathematics

028 
5 
0 
a 10.1007/9783319179391

856 
4 
0 
u https://doi.org/10.1007/9783319179391?nosfx=y
x Verlag
3 Volltext

082 
0 

a 511.4

520 


a 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 wellknown family of radial basis functions (RBFs), which are wellestablished 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 indepth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBFbased solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic timedependent 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
