Quasi-Hermite-Fejér type interpolation of higher order
نویسندگان
چکیده
منابع مشابه
Convergence of Hermite and Hermite-Fejér Interpolation of Higher Order for Freud Weights
We investigate weighted Lp(0 < p <.) convergence of Hermite and Hermite– Fejér interpolation polynomials of higher order at the zeros of Freud orthogonal polynomials on the real line. Our results cover as special cases Lagrange, Hermite– Fejér and Krylov–Stayermann interpolation polynomials. © 2001 Academic Press
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* Correspondence: hsun90@skku. edu Department of Mathematics Education, Sungkyunkwan University Seoul 110-745, Republic of Korea Full list of author information is available at the end of the article Abstract Let R = [0, ∞) and R : R ® R be a continuous function which is the Laguerretype exponent, and pn, r(x), ρ > − 2 be the orthonormal polynomials with the weight wr(x) = x r e. For the zeros ...
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Let wλ(x) := (1−x2)λ−1/2 and P (λ) n be the ultraspherical polynomials with respect to wλ(x). Then we denote by E (λ) n+1 the Stieltjes polynomials with respect to wλ(x) satisfying ∫ 1 −1 wλ(x)P (λ) n (x)E (λ) n+1(x)x dx { = 0, 0 ≤ m < n+ 1, = 0, m = n+ 1. In this paper, we show uniform convergence of the Hermite–Fejér interpolation polynomials Hn+1[·] and H2n+1[·] based on the zeros of the Sti...
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Using the results on the coefficients of Hermite-Fejér interpolations in [5], we investigate convergence of Hermite and Hermite-Fejér interpolation of order m, m = 1, 2, . . . in Lp(0 < p < ∞) and associated product quadrature rules for a class of fast decaying even Erdős weights on the real line.
متن کاملOrthonormal polynomials for generalized Freud-type weights and higher-order Hermite-Feje'r interpolation polynomials
Let Q : R-R be even, nonnegative and continuous, Q0 be continuous, Q040 in ð0;NÞ; and let Q00 be continuous in ð0;NÞ: Furthermore, Q satisfies further conditions. We consider a certain generalized Freud-type weight W 2 rQðxÞ 1⁄4 jxj 2r expð 2QðxÞÞ: In previous paper (J. Approx. Theory 121 (2003) 13) we studied the properties of orthonormal polynomials fPnðW 2 rQ; xÞg N n1⁄40 with the generalize...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1975
ISSN: 0021-9045
DOI: 10.1016/0021-9045(75)90026-x