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. doi:10.1137/0706052. https://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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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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Issue or Number: | 4 | |||||||||
DOI: | 10.1137/0706052 | |||||||||
Record Number: | CaltechAUTHORS:20120921-134826749 | |||||||||
Persistent URL: | https://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: | INVALID USER | |||||||||
Deposited On: | 21 Sep 2012 23:33 | |||||||||
Last Modified: | 09 Nov 2021 23:07 |
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