【摘要】 给出了在非均匀节点情形下用任意k阶B样条作为基函数构造具有高次局部多项式再生性质拟插值的一种方法,并用此方法构造出在无限区间R上具有k-1次多项式再生和k阶收敛阶性质的高精度拟插值(㏑f)(x).进一步地,利用B样条的相关性质由(㏑f)(x)构造出有限区间[a,b]上的高精度拟插值(㏑f)(x).作为数值例子,最后用4阶B样条构造的高精度拟插值(㏑f)(x)逼近一些典型函数以说明其确实具有高精度逼近性质.更多还原

【Abstract】 A method is given to construct quasi-interpolation on non-uniform data points with B-Splines of order k, which possesses polynomial reproducing property of higher degree locally.With the method,a quasi-interpolation (㏑f )(x) is constructed on R,which reproduces polynomials of degree k-1 and has convergence rate of order k. For some properties of B-Splines,the highly accurate quasi-interpolation(㏑f)(x) on[a,b]is gotten from (㏑f)(x).At last,some numerical examples for(㏑f)(x) are presented,which is constructed by B-Splines of order 4.The results are shown to demonstrate the highly accurate approximation property.更多还原