Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-26
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Let wλ(x):=(1-x2)λ-1/2 and Pλ,n be the ultraspherical polynomials with respect to wλ(x).
Then, we denote the Stieltjes polynomials Eλ,n+1 with respect to wλ(x) satisfying ∫-11wλxPλ,nxEλ,n+1xxmdx =0, 0≤m In this paper, we consider the higher-order Hermite-Fejér interpolation operator Hn+1,m based on the zeros of Eλ,n+1 and the higher order extended Hermite-Fejér interpolation operator ℋ2n+1,m based on the zeros of Eλ,n+1Pλ,n. When m is even, we show that Lebesgue constants of these interpolation operators are O(nmax{(1-λ)m-2,0})(0<λ<1) and Onmax1-2λm-2,00<λ<1/2, respectively; that is, ℋ2n+1,m=O(nmax{(1-2λ)m-2,0})(0<λ<1) and Hn+1,m=Onmax1-λm-2,00<λ<1/2. In the case of the Hermite-Fejér interpolation polynomials ℋ2n+1,m[·] for 1/2≤λ<1, we can prove the weighted uniform convergence. In addition, when m is odd, we will show that these interpolations diverge for a certain continuous function on [-1,1], proving that Lebesgue constants of these interpolation operators are similar or greater than log n.
American Psychological Association (APA)
Jung, Hee Sun& Sakai, Ryozi. 2013. Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-480116
Modern Language Association (MLA)
Jung, Hee Sun& Sakai, Ryozi. Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials. Journal of Applied Mathematics No. 2013 (2013), pp.1-15.
https://search.emarefa.net/detail/BIM-480116
American Medical Association (AMA)
Jung, Hee Sun& Sakai, Ryozi. Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-480116
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-480116