On the approximation and saturation of periodic continuous functions by certain trigonometric interpolation polynomials

1976 ◽  
Vol 27 (3-4) ◽  
pp. 323-328 ◽  
Author(s):  
G. Sunouchi
Keyword(s):  
Continuous Functions ◽  
Trigonometric Interpolation ◽  
Interpolation Polynomials

FOURIER FORMULAE FOR EQUIDISTANT HERMITE TRIGONOMETRIC INTERPOLATION

2011 ◽  
Vol 04 (01) ◽  
pp. 127-144 ◽  
Author(s):  
Arnak Poghosyan
Keyword(s):  
Convergence Acceleration ◽  
Lanczos Method ◽  
Trigonometric Interpolation ◽  
Quadrature Formulae ◽  
Interpolation Polynomials ◽  
Exact Constants ◽  
Interpolation Nodes

A sequence of Hermite trigonometric interpolation polynomials with equidistant interpolation nodes and uniform multiplicities is investigated. We derive relatively compact formula that gives the interpolants as functions of the coefficients in the DFTs of the derivative values. The coefficients can be calculated by the FFT algorithm. Corresponding quadrature formulae are derived and explored. Convergence acceleration based on the Krylov-Lanczos method for accelerating both the convergence of interpolation and quadrature is considered. Exact constants of the asymptotic errors are obtained and some numerical illustrations are presented.

scholarly journals On the rate of convergence of interpolation polynomials of Hermite-Fejér type

1978 ◽  
Vol 19 (1) ◽  
pp. 29-37 ◽  
Author(s):  
J. Prasad
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Interpolation Polynomial ◽  
Image Position ◽  
Interpolation Polynomials

For the interpolation polynomial of Hermite-Fejér type An[f] of degree less than or equal to 4n − 1 constructed on the nodes , k = 1, 2, …, n, it is shown that for f ∈ CM(Ω) the inequalityholds where CM(Ω) is the class of continuous functions on [−1, 1] satisfying certain conditions, Ω is a certain modulus of continuity, and c3 and M are positive constants.

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