Published June 1976
| Published
Journal Article
Open
The Effect of Quadrature Errors in the Computation of L^2 Piecewise Polynomial Approximations
- Creators
- Patent, Paul D.
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.
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.Attached Files
Published - PATsiamjna76.pdf
Files
PATsiamjna76.pdf
Files
(1.2 MB)
Name | Size | Download all |
---|---|---|
md5:ed8b2550ad98dc67fdea3467ffdde395
|
1.2 MB | Preview Download |
Additional details
- Eprint ID
- 33029
- Resolver ID
- CaltechAUTHORS:20120808-144219353
- Naval Undersea Center Advanced Graduate Fellowship
- Created
-
2012-08-08Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field