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Approximation Theory of Multivariate Spline Functions in Sobolev Spaces

Schultz, Martin H. (1969) Approximation Theory of Multivariate Spline Functions in Sobolev Spaces. SIAM Journal on Numerical Analysis, 6 (4). pp. 570-582. ISSN 0036-1429. http://resolver.caltech.edu/CaltechAUTHORS:20120921-134826749

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Abstract

In this paper we study some approximation theory questions which arise from the analysis of the discretization error associated with the use of the Rayleigh-Ritz-Galerkin method for approximating the solutions to various types of boundary value problems, cf. [13, [2], [33, [43, [7], [8], [93, [12], [143, [18], [19], [20] and [22]. In particular, we consider upper and lower bounds for the error in approximation of certain families of functions in Sobolev spaces, cf. [15], by functions in finite-dimensional "polynomial spline types" subspaces, cf. [16]. In doing this, we directly generalize, improve, and extend the corresponding results of[1], [17], [18], [19], [20], and [21]. Throughout this paper, the symbol K will be used repeatedly to denote a positive constant, not necessarily the same at each occurrence and the symbol μ will be used repeatedly to denote a nonnegative, continuous function on [0,∞], not necessarily the same at each occurrence.


Item Type:Article
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http://dx.doi.org/10.1137/0706052DOIUNSPECIFIED
http://epubs.siam.org/doi/abs/10.1137/0706052PublisherUNSPECIFIED
Additional Information:© 1969 SIAM. Received by the editors May 22, 1969, and in revised form July 17, 1969. This work was supported in part by the National Science Foundation under Grant GP-11236.
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NSFGP-11236
Record Number:CaltechAUTHORS:20120921-134826749
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120921-134826749
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34286
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:21 Sep 2012 23:33
Last Modified:26 Dec 2012 16:14

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