Approximation under an arc length constraint |
| |
Authors: | L. L. Keener W. H. Ling |
| |
Affiliation: | (1) Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada;(2) Department of Mathematics, Union College, 12308 Schnectady, New York, USA |
| |
Abstract: | Let f C[a, b]. LetP be a subset ofC[a, b], L b – a be a given real number. We say thatp P is a best approximation tof fromP, with arc length constraintL, ifA[p] ba[1 + (p(x))2]dx L andp – f q – f for allq P withA[q] L. represents an arbitrary norm onC[a, b]. The constraintA[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755. |
| |
Keywords: | Primary 41A10 41A50 52A05 |
本文献已被 SpringerLink 等数据库收录! |
|