Optimal interpolation formulas in the space $$W_2^{(m,m-1)}

In the present paper we investigate the problem of construction of the optimal interpolation formulas in the space W2(m,m-1)(0,1). We find the norm of the error functional which gives the upper bound for the error of the interpolation formulas in the space W2(m,m-1)(0,1). Further we get the system o...

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Bibliographic Details
Published in:Calcolo 2019-09, Vol.56 (3), p.1-25, Article 23
Main Authors: Babaev, S. S., Hayotov, A. R.
Format: Article
Language:English
Subjects:
Differential equations
Economic models
Interpolation
Linear equations
Operators (mathematics)
Upper bounds
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Summary:In the present paper we investigate the problem of construction of the optimal interpolation formulas in the space W2(m,m-1)(0,1). We find the norm of the error functional which gives the upper bound for the error of the interpolation formulas in the space W2(m,m-1)(0,1). Further we get the system of linear equations for coefficients of the optimal interpolation formulas. Using the discrete analogue of the differential operator d2mdx2m-d2m-2dx2m-2 and its properties we find explicit formulas for the coefficients of the optimal interpolation formulas. Finally, we give some numerical results which the confirm theoretical results of the paper.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-019-0320-9