國立虎尾科技大學 |

Spherical Radial Basis Functions, Theory and Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Spherical Radial Basis Functions, Theory and Applications/ by Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton.
作者:	Hubbert, Simon.
其他作者:	Le Gia, Quôc Thông.
面頁冊數:	X, 143 p. 7 illus., 3 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Approximation theory. -
電子資源:	https://doi.org/10.1007/978-3-319-17939-1
ISBN:	9783319179391

Spherical Radial Basis Functions, Theory and Applications
Hubbert, Simon.

Spherical Radial Basis Functions, Theory and Applications[electronic resource] /by Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton. - 1st ed. 2015. - X, 143 p. 7 illus., 3 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

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.

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.

ISBN: 9783319179391

Standard No.: 10.1007/978-3-319-17939-1doiSubjects--Topical Terms:

527707
Approximation theory.

LC Class. No.: QA401-425

Dewey Class. No.: 511.4

Spherical Radial Basis Functions, Theory and Applications
LDR:03011nam a22003975i 4500 001 963786
003 DE-He213
005 20200707031227.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319179391 $9 978-3-319-17939-1
024 7 $a 10.1007/978-3-319-17939-1 $2 doi
035 $a 978-3-319-17939-1
050 4 $a QA401-425
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 511.4 $2 23
100 1 $a Hubbert, Simon. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1258823
245 1 0 $a Spherical Radial Basis Functions, Theory and Applications $h [electronic resource] / $c by Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a X, 143 p. 7 illus., 3 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Mathematics, $x 2191-8198
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.
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 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.
650 0 $a Approximation theory. $3 527707
650 0 $a Partial differential equations. $3 1102982
650 0 $a Numerical analysis. $3 527939
650 0 $a Global analysis (Mathematics). $3 1255807
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a Geophysics. $3 686174
650 1 4 $a Approximations and Expansions. $3 672153
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Numerical Analysis. $3 671433
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 2 4 $a Geophysics/Geodesy. $3 668510
700 1 $a Le Gia, Quôc Thông. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1258824
700 1 $a Morton, Tanya M. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1258825
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319179407
776 0 8 $i Printed edition: $z 9783319179384
830 0 $a SpringerBriefs in Mathematics, $x 2191-8198 $3 1255329
856 4 0 $u https://doi.org/10.1007/978-3-319-17939-1
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)