Abstract
In this article the modelling of the nonpolynomial integro-dierential splines is discussed. This splines interpolate function and its derivatives in knots of a grid and provide concurrence of integral size from approximated function and size of integral from spline on the set interval. Here explosive, continuous, and continuously dierentiated several times basic splines are constructed. They allow to solve problems of the construction of approximation if we know the values of the function and its derivatives in knots of a grid and in the additional assumption that values of integrals from approached function on net intervals are known. Estimations errors are resulted and examples of splines are given
Highlights
ISSN 2078-9181 (print), ISSN 2078-9599 (online) ïîñòðîèì q u(x) = δ1 k+sα u(α)(xj ) ωj,α(x)+
solve problems of the construction of approximation if we know the values of the function
Interpolation polynomial splines with the local support have recommended itself
Summary
ISSN 2078-9181 (print), ISSN 2078-9599 (online) ïîñòðîèì q u(x) = δ1 k+sα u(α)(xj ) ωj,α(x)+  ÷àñòíîñòè, äëÿ ôóíêöèè ωk,α(x) íà ïðîìåæóòêå [xk, xk+1] Xk−1 xk ãÇåäáåðñàüèω÷åkè(õx)ó, ðià=âí−åí1è,é1,, îïðåäåëÿþòñÿ èç ñèñòåìû ïîëó÷àåìûõ èç óñëîâèé ëèíåéíûõ àëu(x) ≡ u(x), íïàðè[Ñxuèk(,ñxxò)åkì+=1à]φ.ó1ð(àxâ),íφåí2(èxé),èãìäåååòφiâ(èxä), i = 1, 2 ÷åáûøåâñêàÿ ñèñòåìà xk xk+1 φi(x)dxωk(x) + Îïðåäåëèòåëü ýòîé ñèñòåìû äëÿ ïîëèíîìèàëüíûõ áàçèñíûõ ôóíêöèé xk+1 − xk xk − xk−1 (x2k+1 − x2k)/2 (x2k − x2k−1)/2 ðîïàâðååíäå(ëxèkò+å1ë−ü îxòkë−è1÷)å(xíkî−ò íxókë−ÿ1.)(xk − . Ïðè φ1 = 1, φ2 = x ïîëó÷àåì ωk(th
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