Patent, Paul D. (1976) The Effect of Quadrature Errors in the Computation of L^2 Piecewise Polynomial Approximations. SIAM Journal on Numerical Analysis, 13 (3). pp. 344-361. ISSN 0036-1429. doi:10.1137/0713031. https://resolver.caltech.edu/CaltechAUTHORS:20120808-144219353
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Abstract
In this paper we investigate the L^2 piecewise polynomial approximation problem. L^2 bounds for the derivatives of the error in approximating sufficiently smooth functions by polynomial splines follow immediately from the analogous results for polynomial spline interpolation. We derive L^2 bounds for the errors introduced by the use of two types of quadrature rules for the numerical computation of L^2 piecewise polynomial approximations. These bounds enable us to present some asymptotic results and to examine the consistent convergence of appropriately chosen sequences of such approximations. Some numerical results are also included.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1976 Society for Industrial and Applied Mathematics. Received by the editors September 10, 1974. This research represents part of the author's doctoral dissertation submitted to the Graduate School of the California Institute of Technology, Pasadena, California. The author was supported in his studies by a Naval Undersea Center Advanced Graduate Fellowship. The author wishes to thank Professors H. B. Keller and M. H. Schultz for their guidance in the investigation of this problem and the interpretation of the results. | |||||||||
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| Issue or Number: | 3 | |||||||||
| DOI: | 10.1137/0713031 | |||||||||
| Record Number: | CaltechAUTHORS:20120808-144219353 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120808-144219353 | |||||||||
| Official Citation: | The Effect of Quadrature Errors in the Computation of L^2 Piecewise Polynomial Approximations Paul D. Patent SIAM J. Numer. Anal. 13-3 (1976), pp. 344-361 (18 pages) http://dx.doi.org/10.1137/0713031 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 33029 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 08 Aug 2012 22:50 | |||||||||
| Last Modified: | 09 Nov 2021 21:31 |
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