Best polynomial approximation on the triangle

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

1 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)63-78
Journal / PublicationJournal of Approximation Theory
Volume241
Online published18 Jan 2019
Publication statusPublished - May 2019

Abstract

Let En(f)α,β,γ denote the error of best approximation by polynomials of degree at most n in the space L2(ϖα,β,γ) on the triangle {(x, y) : x≥ 0, x + y ≤ 1}, where ϖα,β,γ(x, y) ≔ xαyβ (1 − xy)γ for α,β,γ > −1. Our main result gives a sharp estimate of En(f)α,β,γ in terms of the error of best approximation for higher order derivatives of f in appropriate Sobolev spaces. The result also leads to a characterization of En(f)α,β,γ by a weighted K-functional.

Research Area(s)

  • Best polynomial approximation, K-functional, Orthogonal expansion, Triangle

Citation Format(s)

Best polynomial approximation on the triangle. / Feng, Han; Krattenthaler, Christian; Xu, Yuan.
In: Journal of Approximation Theory, Vol. 241, 05.2019, p. 63-78.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review