Аннотация:
The paper deals with approximative and form–retaining properties of the local parabolic splines of the form $S(x)=\sum\limits_j y_j B_2
(x-jh), \ (h>0),$ where $B_2$ is a normalized parabolic spline with the uniform nodes and functionals $y_j=y_j(f)$ are given for an
arbitrary function $f$ defined on $\mathbb{R}$ by means of the equalities $$y_j=\frac{1}{h_1}\int\limits_{\frac{-h_1}{2}}^{\frac{h_1}{2}}
f(jh+t)dt \quad (j\in\mathbb{Z}). $$ On the class $W^2_\infty$ of functions under $0<h_1\leq 2h$, the approximation error value is
calculated exactly for the case of approximation by such splines in the uniform metrics.
Ключевые слова:
Local parabolic splines, Approximation, Mean.
Реферативные базы данных:
Тип публикации:
Статья
Язык публикации: английский
Образец цитирования:
Elena V. Strelkova, “Approximation by local parabolic splines constructed on the basis of interpolationin the mean”, Ural Math. J., 3:1 (2017), 81–94
\RBibitem{Str17}
\by Elena~V.~Strelkova
\paper Approximation by local parabolic splines constructed on the basis of interpolationin the mean
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 1
\pages 81--94
\mathnet{http://mi.mathnet.ru/umj35}
\crossref{https://doi.org/10.15826/umj.2017.1.007}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR3684227}
\elib{https://elibrary.ru/item.asp?id=29728777}
В. Т. Шевалдин, “О локальных параболических интерполяционных сплайнах Фавара с дополнительными узлами”, Ж. вычисл. матем. и матем. физ., 63:6 (2023), 979–986; V. T. Shevaldin, “On Favard local parabolic interpolating splines with additional knots”, Comput. Math. Math. Phys., 63:6 (2023), 1045–1051
Цитирование в формате AMSBIB
Обратная связь: