Unicity in piecewise polynomial -approximation via an algorithm |
| |
Authors: | R C Gayle J M Wolfe |
| |
Institution: | Department of Science and Mathematics, Montana State University-Northern, P. O. Box 7751, Havre, Montana 59501 ; Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222 |
| |
Abstract: | Our main result shows that certain generalized convex functions on a real interval possess a unique best approximation from the family of piecewise polynomial functions of fixed degree with varying knots. This result was anticipated by Kioustelidis in 11]; however the proof given there is nonconstructive and uses topological degree as the primary tool, in a fashion similar to the proof the comparable result for the case in 5]. By contrast, the proof given here proceeds by demonstrating the global convergence of an algorithm to calculate a best approximation over the domain of all possible knot vectors. The proof uses the contraction mapping theorem to simultaneously establish convergence and uniqueness. This algorithm was suggested by Kioustelidis 10]. In addition, an asymptotic uniqueness result and a nonuniqueness result are indicated, which analogize known results in the case. |
| |
Keywords: | Polynomial approximation Lagrange interpolation $L^{1}$ approximation |
|
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 |
| 点击此处可从《Mathematics of Computation》下载免费的PDF全文 |
|