On the Eigenstructure of the Modified Bernstein Operators. (22nd November 2022)

• Record Type: Journal Article
• Authors: Gürel Yılmaz, Övgü; Ostrovska, Sofiya; Turan, Mehmet
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 16(2022)
• Page Start: 1821
• Page End: 1835
• Publication Date: 2022-11-22
• Subjects: Bernstein operators -- eigenvalues -- eigenvectors -- modified Bernstein operators -- Stirling numbers; 47A75 -- 47B38; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2136695
• Languages: English
• ISSNs: 0163-0563

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.