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1
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Obtaining a banded system of equations in complete spline interpolation problem via B-spline basis

100%
Volkov Y.
Open Mathematics
|
2012
|
tom 10
|
nr 1
352-356
EN
We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.
2
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An extended Prony’s interpolation scheme on an equispaced grid

100%
Karalienė D., Navickas Z., Čiegis R., Ragulskis M.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
An interpolation scheme on an equispaced grid based on the concept of the minimal order of the linear recurrent sequence is proposed in this paper. This interpolation scheme is exact when the number of nodes corresponds to the order of the linear recurrent function. It is shown that it is still possible to construct a nearest mimicking algebraic interpolant if the order of the linear recurrent function does not exist. The proposed interpolation technique can be considered as the extension of the Prony method and can be useful for describing noisy and defected signals.
3
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A note on the rate of convergence for Chebyshev-Lobatto and Radau systems

84%
Berriochoa E., Cachafeiro A., Díaz J., Martínez E.
Open Mathematics
|
2016
|
tom 14
|
nr 1
156-166
EN
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
4
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Harmonic interpolation based on Radon projections along the sides of regular polygons

84%
Georgieva I., Hofreither C., Koutschan C., Pillwein V., Thanatipanonda T.
Open Mathematics
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2013
|
tom 11
|
nr 4
609-620
EN
Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.
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