基于B样条构造高精度拟插值  

Construction of Highly Accurate Quasi-Interpolation Operators by B-Splines

作　　者：徐志伟[1] 吴宗敏[1] 

机构地区：[1]复旦大学数学科学学院,上海200433

出　　处：《复旦学报（自然科学版）》2010年第4期506-512,共7页Journal of Fudan University：Natural Science

基　　金：国家重点基础研究发展计划(973计划)资助项目(2006cb303102);上海市科学技术委员会资助项目(08DZ2271900)

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.A method is given to construct quaskinterpolation on nowuniform data points with B-Splines of order k, which possesses polynomial reproducing property of higher degree locally. With the method, a quasi-interpolation （hf） （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 （hf）（x） on [a, b] is gotten from （hf） （x）. At last, some numerical examples for （hf）（x） are presented, which is constructed by B-Splines of order 4. The results are shown to demonstrate the highly accurate approximation property.

关 键 词：非均匀B样条 多项式再生 高精度拟插值 

分 类 号：O241.8[理学—计算数学] O174.4[理学—数学]