Asymptotic formulas for Lebesgue functions corresponding to the family of Lagrange interpolation polynomials

2017 ◽  
Vol 102 (1-2) ◽  
pp. 111-123
Author(s):  
I. A. Shakirov
Keyword(s):  
Lagrange Interpolation ◽  
Asymptotic Formulas ◽  
The Family ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials ◽  
Lebesgue Functions

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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