LOCAL LINEAR TRIGONOMETRIC FUNDAMENTAL SPLINES FOR APPROXIMATING SOME GEOMETRIC CURVES IN THE PLANE
DOI:
https://doi.org/10.55640/Keywords:
Approximation, interpolation, basis functions, fundamental splines, optimal interpolation formula, geometric curves, Sobolev method.Abstract
In this work, new local trigonometric fundamental splines are constructed for the integration of some geometric curves on a plane. In this case, we use the coefficients of the trigonometric optimal interpolation formula, constructed using the Sobolev method in a known Hilbert space of differentiable functions. In addition, we will present and prove the theorem expressing their main property.
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1.Hayotov A. R., Doniyorov N. N. Construction of an optimal interpolation Formula Exact for trigonometric functions. Modern problems of applied mathematics and information technology, AIP Conference Proceedings, 2024. Vol.300. Pp.06051-1-06051-11, https://doi.org/10.1063/5.0199916.
2.Завьялов Ю. С., Квасов Б. И., Мирошниченко В. Л. Методы сплайн-функций. М., Наука, 1980. -352 с.
3.Zhilin Li, Zhonghua Qiao, Tao Tang. Numerical Solution of Differential Equations. Cambridge University Press, 2018.
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