Construction of Dm -splines in space L2m(0,1) by Sobolev method
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ISSN: 0096-3003
E-ISSN: 1873-5649
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Abstract
In the present paper, using S.L. Sobolev's method, interpolation $D^m$- splines that minimizes the expression $\int_0^1(\varphi^{(m)}(x))^2dx$ in the $L_2^{(m)}(0,1)$ space are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation spline is exact for polynomials of degree $m-1$. Some numerical experiments are presented. Moreover the connection between the obtained interpolation splines and the optimal quadrature formulas are shown
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A. Cabada, A.R. Hayotov, Kh.M. Shadimetov, Construction of Dm-splines in L2(m)(0,1) space by Sobolev method, Applied Mathematics and Computation, Volume 244, 2014, Pages 542-551, ISSN 0096-3003, https://doi.org/10.1016/j.amc.2014.07.033. (https://www.sciencedirect.com/science/article/pii/S0096300314009904)
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https://doi.org/10.1016/j.amc.2014.07.033Sponsors
The present work was done in the University of Santiago de Compostela, Spain. A.R. Hayotov thanks the program Erasmus Mundus Action 2, Stand 1, Lot 10, Marco XXI for financial support (project number: 204513-EM-1-2011-1-DE-ERA MUNDUS-EMA21)
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