推广的二元三角插值算子的收敛与饱和  

On convergence and saturation of generalized bivariate trigonometric interpolation operators

作　　者：叶志萍[1] 王小刚[1] 

机构地区：[1]北方民族大学基础教学部,宁夏银川750021

出　　处：《安徽大学学报（自然科学版）》2011年第1期5-9,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10961001);宁夏省科技厅自然科学基金资助项目(NZ0846);北方民族大学科研基金资助项目(2010Y037)

摘　　要：构造了不依赖于结点组的更广的一类二元Fourier插值算子和二元离散的Fourier插值算子,估计了两类算子的收敛阶,并且证明了对于二元连续周期函数类来讲,该收敛阶是最优的.更进一步讨论了这两类算子的饱和问题,得到了饱和阶的估计.在收敛阶和饱和阶的度量上,论文结果与以往文献中的结果是一致的.The problem constructed here were the uniform convergence and saturation of a kind of generalized bivariate trigonometric interpolation operators, which independent to the choice of node, including bivariate interpolation operator of Fourier operators and the discrete Fourier operators. The convergence order of the approximation would be optimal for a body of bivariate continuous and period functions. Moreover, saturation order was discussed and estimated. The results were coincident in the measure of saturation order of other papers.

关 键 词：二元 三角插值 收敛阶 饱和阶 

分 类 号：O174.41[理学—数学]