摘要
考虑由扰动数据重构原函数的导数问题。利用积分算子,提出一种新的构造近似导数的方法,与Groetsch提出的求导方法相比较,提高了稳定近似导数的收敛率,在一定的条件下近似已知函数的导数收敛率可以达到O(δ67),δ为近似数据的误差界。证明了上述收敛率在某种意义下是最优的。
The problem to reconstruct the derivative of a function from noisy data is considered. A new stable method for differentiation of approximate specified functions is presented by using integral operator. The convergence rate of the stable approximate differentiation is improved and the improved estimate is O （δ^6/7） under some conditions, as compared with the Groetsch＇ s method for approximate differentiation, δ is error bound of approximate data, and it is proved that such convergence rate can be optimal under some conditions.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2009年第1期51-54,共4页
Journal of Natural Science of Heilongjiang University
基金
黑龙江省自然科学基金资助项目(LBH-Q05114)
黑龙江省教育厅资助项目(11511276)
关键词
不适定问题
近似微商
收敛率
ill - posed problem
approximate differentiation
convergence rate
