On the Degree of Approximation by Monotone Polynomials

Authors

Vasant A. Ubhaya

Document Type

Report

Publication Date

5-1-1976

Abstract

This article considers the problem of approximating a continuous function defined on an interval by polynomials which are monotone nondecreasing there. Upper and lower bounds on the degree of approximation are obtained in terms of moduli of monotonicity, a concept which the author introduced in an earlier article [12]. Certain asymptotic results are also established. One of the results of this article shows that when f is continuous but not nondecreasing, En(f), the degree of approximation of f by monotone polynomials of degree at most n, converges to a positive number as n→∞, at a rate which is at least linear or geometric. The complementary case when f is continuous and nondecreasing has been considered earlier in the literature.

Keywords

Operations research, Approximation theory, Functions, Polynomials, Asymptotic expansions

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 410

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

Recommended Citation

Ubhaya, Vasant A., "On the Degree of Approximation by Monotone Polynomials" (1976). Research Reports from the Department of Operations. 364.
https://commons.case.edu/wsom-ops-reports/364