On Asymptotics for the Uniform Norms of the Lagrange Interpolation Polynomials Corresponding to Extended Chebyshev Nodes

1988 ◽  
Vol 25 (2) ◽  
pp. 461-469 ◽  
Author(s):  
R. Günttner
Keyword(s):  
Lagrange Interpolation ◽  
Chebyshev Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Interpolation Polynomials

scholarly journals An extension of the Grünwald–Marcinkiewicz interpolation theorem

2001 ◽  
Vol 63 (2) ◽  
pp. 299-320 ◽  
Author(s):  
T. M. Mills ◽  
P. Vértesi
Keyword(s):  
Lagrange Interpolation ◽  
Interpolation Theorem ◽  
Higher Order ◽  
Classical Theorem ◽  
Chebyshev Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Marcinkiewicz Interpolation Theorem ◽  
Interpolation Polynomials ◽  
Special Case

Just over 60 years ago, G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. The main result of the present paper is an extension of their now classical theorem. In particular, we shall show that this divergence phenomenon occurs for odd higher order Hermite–Fejér interpolation polynomials of which Lagrange interpolation polynomials form one special case.

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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