發(fā)布時間：2018-09-11 20:22

【摘要】：將數(shù)值計算中的函數(shù)插值和外形設(shè)計中的參數(shù)曲線插值相結(jié)合,提出構(gòu)造具有指定多項式重構(gòu)精度的函數(shù)插值和具有指定連續(xù)階的參數(shù)曲線插值的一般方法.該方法以Hermite插值的基本形式為橋梁,首先以用于函數(shù)插值時達到指定的精度為目標來推導(dǎo)基本形式中的導(dǎo)向量表達式,通過解方程獲取導(dǎo)向量中的系數(shù);然后將導(dǎo)向量代入Hermite插值的基本形式,并將其按照插值數(shù)據(jù)點進行整理,得出插值基函數(shù)表達式;最后給出以插值數(shù)據(jù)點和插值基函數(shù)的線性組合形式表達的插值曲線.數(shù)值實驗結(jié)果表明,曲線形狀可以固定也可以做局部調(diào)整,所給2n+1次Hermite插值多項式的重構(gòu)精度一般會超過n次.
[Abstract]:Combining the function interpolation in the numerical calculation with the parameter curve interpolation in the shape design, a general method of constructing the function interpolation with the specified polynomial reconstruction accuracy and the parameter curve interpolation with the specified continuous order is proposed. In this method, the basic form of Hermite interpolation is used as the bridge. Firstly, the expression of the guiding quantity in the basic form is deduced with the objective of achieving the specified precision when the function is interpolated, and the coefficients in the guiding quantity are obtained by solving the equation. Then the guide quantity is substituted into the basic form of Hermite interpolation and arranged according to the interpolation data points to obtain the interpolation basis function expression. Finally the interpolation curve expressed in the form of linear combination of interpolation data points and interpolation basis functions is given. The numerical results show that the shape of the curve can be fixed or locally adjusted, and the reconstruction accuracy of the 2n-1 Hermite interpolation polynomial is generally higher than that of n.
【作者單位】： 東華理工大學(xué)理學(xué)院;中南大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院;
【基金】：國家自然科學(xué)基金(11261003,11271376,60970097) 江西省自然科學(xué)基金(20161BAB211028) 江西省教育廳科技項目(GJJ160558)
【分類號】：TP391.7

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