On the Eigenstructure of the Modified Bernstein Operators

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2022-10-28 DOI:10.1080/01630563.2022.2136695

Övgü Gürel Yılmaz, Sofiya Ostrovska, M. Turan

引用次数: 0

Abstract

Abstract Starting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Qn have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well.

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关于修正Bernstein算子的特征结构

摘要从Cooper和Waldron于2000年发表的著名著作开始，许多研究人员对各种Bernstein型算子的本征结构进行了研究。本文研究了修正Bernstein算子Qn的特征值和特征向量。这些算子是由S·N·伯恩斯坦本人在1932年提出的，目的是加速光滑函数的近似率。在此，建立了本征值和相应本征多项式的显式公式及其极限行为。结果表明，尽管一些结果与Bernstein算子的结果相似，但也有本质上不同的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.