具有指定多项式重构精度和连续阶的插值曲线构造方法
发布时间：2018-09-11 20:22
【摘要】：将数值计算中的函数插值和外形设计中的参数曲线插值相结合,提出构造具有指定多项式重构精度的函数插值和具有指定连续阶的参数曲线插值的一般方法.该方法以Hermite插值的基本形式为桥梁,首先以用于函数插值时达到指定的精度为目标来推导基本形式中的导向量表达式,通过解方程获取导向量中的系数;然后将导向量代入Hermite插值的基本形式,并将其按照插值数据点进行整理,得出插值基函数表达式;最后给出以插值数据点和插值基函数的线性组合形式表达的插值曲线.数值实验结果表明,曲线形状可以固定也可以做局部调整,所给2n+1次Hermite插值多项式的重构精度一般会超过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.
【作者单位】： 东华理工大学理学院;中南大学数学与统计学院;
【基金】：国家自然科学基金(11261003,11271376,60970097) 江西省自然科学基金(20161BAB211028) 江西省教育厅科技项目(GJJ160558)
【分类号】：TP391.7
[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.
【作者单位】： 东华理工大学理学院;中南大学数学与统计学院;
【基金】：国家自然科学基金(11261003,11271376,60970097) 江西省自然科学基金(20161BAB211028) 江西省教育厅科技项目(GJJ160558)
【分类号】：TP391.7
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