scholarly journals On the Lagrange interpolation polynomials of entire functions

1984 ◽  
Vol 41 (2) ◽  
pp. 170-178 ◽  
Author(s):  
Radwan Al-Jarrah
Keyword(s):  
Lagrange Interpolation ◽  
Entire Functions ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials

scholarly journals Asymptotics of Polynomial Interpolation and the Bernstein Constants

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Michael Revers
Keyword(s):  
Exponential Type ◽  
Chebyshev Polynomials ◽  
Lagrange Interpolation ◽  
Entire Functions ◽  
Polynomial Interpolation ◽  
Asymptotic Bounds ◽  
Functions Of Exponential Type ◽  
Chebyshev Interpolation ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials

AbstractIt is well known that the interpolation error for $$\left| x\right| ^{\alpha },\alpha >0$$ x α , α > 0 in $$L_{\infty }\left[ -1,1\right] $$ L ∞ - 1 , 1 by Lagrange interpolation polynomials based on the zeros of the Chebyshev polynomials of first kind can be represented in its limiting form by entire functions of exponential type. In this paper, we establish new asymptotic bounds for these quantities when $$\alpha $$ α tends to infinity. Moreover, we present some explicit constructions for near best approximation polynomials to $$\left| x\right| ^{\alpha },\alpha >0$$ x α , α > 0 in the $$L_{\infty }$$ L ∞ norm which are based on the Chebyshev interpolation process. The resulting formulas possibly indicate a general approach towards the structure of the associated Bernstein constants.

scholarly journals Interpolation Polynomials of Entire Functions for Erdös-Type Weights

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Gou Nakamura ◽  
Ryozi Sakai ◽  
Noriaki Suzuki
Keyword(s):  
Quadrature Formula ◽  
Lagrange Interpolation ◽  
Entire Functions ◽  
Error Terms ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials

Letℝ=(−∞,∞), and letQ∈C1(ℝ):ℝ→[0,∞)be an even function. In this paper, we consider some Lagrange interpolation polynomials and the Gauss-Jacobi quadrature formula of entire functions associated with Erdös-type weightsw(x)=e−Q(x),x∈ℝ, and we will estimate the error terms.

scholarly journals On Lagrange interpolation with equally spaced nodes

2000 ◽  
Vol 62 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Michael Revers
Keyword(s):  
Rate Of Convergence ◽  
Lagrange Interpolation ◽  
End Points ◽  
Quantitative Version ◽  
Equidistant Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Exact Rate Of Convergence

A well-known result due to S.N. Bernstein is that sequence of Lagrange interpolation polynomials for |x| at equally spaced nodes in [−1, 1] diverges everywhere, except at zero and the end-points. In this paper we present a quantitative version concerning the divergence behaviour of the Lagrange interpolants for |x|3 at equidistant nodes. Furthermore, we present the exact rate of convergence for the interpolatory parabolas at the point zero.

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