Spherical radial basis functions, theory and applications [Documento electrónico] / Simon Hubbert, Quôc Thông Lê Gia, Tanya M. Morton
Language: eng.Country: US - United States of America.Publication: Cham : Springer International Publishing, 2015Description: X, 143 p. 7 il.ISBN: 978-3-319-17939-1.Series: Springer briefs in mathematicsSubject - Topical Name: Teoria da aproximação | Equações diferenciais parciais | Análise numérica | Análise global (Matemática) | Geofísica Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA221.SPR FCT 96096 Approximation theory XIII, San Antonio 2010 | QA221.SPR FCT 96104 Mathematics of approximation | QA221.SPR FCT 96575 Analysis on h-harmonics and dunkl transforms | QA221.SPR FCT 96827 Spherical radial basis functions, theory and applications | QA221.SPR FCT 97038 Approximation by max-product type operators | QA221.SPR FCT 97581 Progress in approximation theory and applicable complex analysis, In memory of Q.I. Rahman | QA221.SPR FCT 97748 Bernstein operators and their properties |
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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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