摘要
研究了几类在给出全部和部分信息时线性泛函和线性算子的反演问题.介绍了最优反演理论的基本结果,特别是最优反演方法的构造.作为例子,讨论了在给出部分傅里叶系数时反演函数和函数的导数问题.
The paper is concerned with recovery problems of linear functionals and operators from precise and noisy information. We present several basic results from the theory of optimal recovery. Special attention is paid to the construction of optimal recovery methods. As an example of application, the problem of recovery of functions and their derivatives from the inaccurate Fourier coefficients is considered.
出处
《应用数学与计算数学学报》
2016年第4期459-481,共23页
Communication on Applied Mathematics and Computation
基金
Project supported by the financial support of the Russian Foundation for Basic Research(14-01-00456,14-01-00744)
