LEADER 04745nam 22008055 450 001 9910299768503321 005 20200707031227.0 010 $a3-319-17939-X 024 7 $a10.1007/978-3-319-17939-1 035 $a(CKB)3710000000414279 035 $a(EBL)2095454 035 $a(SSID)ssj0001501732 035 $a(PQKBManifestationID)11901936 035 $a(PQKBTitleCode)TC0001501732 035 $a(PQKBWorkID)11447660 035 $a(PQKB)10334645 035 $a(DE-He213)978-3-319-17939-1 035 $a(MiAaPQ)EBC2095454 035 $a(PPN)186027559 035 $a(EXLCZ)993710000000414279 100 $a20150513d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpherical Radial Basis Functions, Theory and Applications$b[electronic resource] /$fby Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (150 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a3-319-17938-1 320 $aIncludes bibliographical references. 327 $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. 330 $aThis book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aApproximation theory 606 $aPartial differential equations 606 $aNumerical analysis 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aGeophysics 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aGeophysics/Geodesy$3https://scigraph.springernature.com/ontologies/product-market-codes/G18009 615 0$aApproximation theory. 615 0$aPartial differential equations. 615 0$aNumerical analysis. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aGeophysics. 615 14$aApproximations and Expansions. 615 24$aPartial Differential Equations. 615 24$aNumerical Analysis. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aGeophysics/Geodesy. 676 $a515.53 700 $aHubbert$b Simon$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755599 702 $aLe Gia$b Quôc Thông$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMorton$b Tanya M$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299768503321 996 $aSpherical Radial Basis Functions, Theory and Applications$92540386 997 $aUNINA