On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions

The question of adaptive approximation by splines has been studied for a number of years by various authors. The results obtained have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential...

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Main Author:	Babenko, Yuliya
Other Authors:	Larry Schumaker
Format:	Others
Language:	en
Published:	VANDERBILT 2006
Subjects:	Mathematics
Online Access:	http://etd.library.vanderbilt.edu/available/etd-05012006-144209/

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spelling	ndltd-VANDERBILT-oai-VANDERBILTETD-etd-05012006-1442092013-01-08T17:16:10Z On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions Babenko, Yuliya Mathematics The question of adaptive approximation by splines has been studied for a number of years by various authors. The results obtained have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others. In this dissertation we investigate some questions of adaptive approximation by various classes of splines (linear, multilinear, biquadratic) with free knots. In particular, we will study the asymptotic behavior of the optimal error of weighted approximation in different norms by interpolating splines from these classes. The proofs lead to the construction of asymptotically optimal simplicial or box partitions of the domain for interpolation by linear and multilinear splines, respectively. In addition, applications to quadrature formulas are considered. Larry Schumaker VANDERBILT 2006-05-03 text application/pdf http://etd.library.vanderbilt.edu/available/etd-05012006-144209/ http://etd.library.vanderbilt.edu/available/etd-05012006-144209/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Vanderbilt University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.
collection	NDLTD
language	en
format	Others
sources	NDLTD
topic	Mathematics
spellingShingle	Mathematics Babenko, Yuliya On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
description	The question of adaptive approximation by splines has been studied for a number of years by various authors. The results obtained have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others. In this dissertation we investigate some questions of adaptive approximation by various classes of splines (linear, multilinear, biquadratic) with free knots. In particular, we will study the asymptotic behavior of the optimal error of weighted approximation in different norms by interpolating splines from these classes. The proofs lead to the construction of asymptotically optimal simplicial or box partitions of the domain for interpolation by linear and multilinear splines, respectively. In addition, applications to quadrature formulas are considered.
author2	Larry Schumaker
author_facet	Larry Schumaker Babenko, Yuliya
author	Babenko, Yuliya
author_sort	Babenko, Yuliya
title	On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
title_short	On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
title_full	On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
title_fullStr	On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
title_full_unstemmed	On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
title_sort	on the asymptotic behavior of the optimal error of spline interpolation of multivariate functions
publisher	VANDERBILT
publishDate	2006
url	http://etd.library.vanderbilt.edu/available/etd-05012006-144209/
work_keys_str_mv	AT babenkoyuliya ontheasymptoticbehavioroftheoptimalerrorofsplineinterpolationofmultivariatefunctions
_version_	1716533081318359040

On the asymptotic behavior of the optimal error of spline interpolation of multivariate functions

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