Approximation Theory of Multivariate Spline Functions in Sobolev Spaces
- Creators
- Schultz, Martin H.
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.
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.Attached Files
Published - SCHUsiamjna69b.pdf
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Additional details
- Eprint ID
- 34286
- Resolver ID
- CaltechAUTHORS:20120921-134826749
- GP-11236
- NSF
- Created
-
2012-09-21Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field