Convergence of lacunary trigonometric interpolation on equidistant nodes

1982 ◽  
Vol 39 (1-3) ◽  
pp. 27-37 ◽  
Author(s):  
S. Riemenschneider ◽  
A. Sharma ◽  
P. W. Smith
Keyword(s):  
Trigonometric Interpolation ◽  
Equidistant Nodes

SOME 2-PERIODIC TRIGONOMETRIC INTERPOLATION PROBLEMS ON EQUIDISTANT NODES

Analysis ◽  
1991 ◽  
Vol 11 (2-3) ◽  
Author(s):  
A. SHARMA ◽  
J . SZABADOS ◽  
R . S . VARGA
Keyword(s):  
Trigonometric Interpolation ◽  
Interpolation Problems ◽  
Equidistant Nodes

LACUNARY TRIGONOMETRIC INTERPOLATION ON EQUIDISTANT NODES

Analysis ◽  
1986 ◽  
Vol 6 (2-3) ◽  
Author(s):  
A. Jakimovski ◽  
A. Sharma
Keyword(s):  
Trigonometric Interpolation ◽  
Equidistant Nodes

scholarly journals Trigonometric interpolation

1992 ◽  
Vol 35 (3) ◽  
pp. 457-472
Author(s):  
T. N. T. Goodman ◽  
A. Sharma
Keyword(s):  
Interpolation Problem ◽  
Arbitrary Sequence ◽  
Trigonometric Interpolation ◽  
Equidistant Nodes ◽  
Explicit Expressions

We consider interpolation at 2n equidistant nodes in [0,π) from the space ℱN spanned by sines and cosines of odd multiples of x. This interpolation problem is shown to be correct for an arbitrary sequence of derivatives specified at all the nodes. Explicit expressions for the fundamental polynomials are obtained and it is shown that under mild smoothness assumptions on the function f interpolant from ℱN converges uniformly to f as the node spacing goes to zero.

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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