The Coeffisients of the Spline Minimizing Semi Norm in K2(P3)

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DOI: https://doi.org/10.28924/2291-8639-23-2025-7
Published: Jan 2, 2025
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A.R. Hayotov, F.A. Nuraliev, G.Sh. Abdullaeva, The Coeffisients of the Spline Minimizing Semi Norm in K2(P3), Int. J. Anal. Appl., 23 (2025), 7.

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A.R. Hayotov, F.A. Nuraliev, G.Sh. Abdullaeva

Abstract

Our goal is to construct an approximation of the unknown function f by Sobolev’s method, we construct an approximation form of unknown function by interpolation splines minimizing the semi norm in K2(P3) Hilbert space. Explicit formulas for coefficients of the interpolation splines are obtained. The resulting interpolation spline is exact for the hyperbolic functions and constant. In the last section, we obtain several absolute errors graph in interpolating functions with the sixth order algebraic-hyperbolic spline, and we compare absolute errors of cubic spline and algebraic-hyperbolic in interpolating several functions. Numerical results show that the sixth-order spline interpolates the functions with higher accuracy than the cubic spline.

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