02989nmm a2200397 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001900139245014300158250001700301260005600318300005900374505024400433653001500677653002300692653003400715653002300749653002800772653002500800653002700825653003400852653004600886653002700932700003500959700003100994041001901025989003601044490003401080028003001114856007201144082001001216520136501226EB001033722EBX0100000000000000082724400000000000000.0cr|||||||||||||||||||||150601 ||| eng a97833191793911 aHubbert, Simon00aSpherical Radial Basis Functions, Theory and ApplicationshElektronische Ressourcecby Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton a1st ed. 2015 aChambSpringer International Publishingc2015, 2015 aX, 143 p. 7 illus., 3 illus. in colorbonline resource0 aMotivation 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 aGeophysics aNumerical Analysis aApproximations and Expansions aNumerical analysis aManifolds (Mathematics) aApproximation theory aDifferential Equations aGlobal analysis (Mathematics) aGlobal Analysis and Analysis on Manifolds aDifferential equations1 aLe Gia, Quôc Thônge[author]1 aMorton, Tanya M.e[author]07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aSpringerBriefs in Mathematics50a10.1007/978-3-319-17939-140uhttps://doi.org/10.1007/978-3-319-17939-1?nosfx=yxVerlag3Volltext0 a511.4 aThis 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