Approximation of functions of the class $$H_{\omega _2 }^2 $$ by trigonometric interpolation polynomials with equally spaced nodes

1980 ◽  
Vol 27 (6) ◽  
pp. 439-445
Author(s):  
Yu. R. Vainerman
Keyword(s):  
Trigonometric Interpolation ◽  
Approximation Of Functions ◽  
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.

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