一类基于积分平均值的函数重构

考虑一类基于带有扰动的积分平均值的函数重构方法,从抽象算子方程的角度分析解决此类问题.证明解算子与网络步长无关的有界性,从而证明所讨论的问题的适定性,表明求解过程不需要正则化,大大简化了算法.最后,给出数值例子验证所讨论的方法的有效性.

A Type of Reconstruction Methods of Function Based on Integral Average Values

A reconstruction problem of function from integral average values with perturbation is considered,and propose a type of reconstruction method.From the abstract operator equation,we analyze and solve this type of problem,and show that the solution operator is bounded regardless of the grid size.Therefore the problem under consideration is well-posed.The method of solving this problem does not need regularization,thus greatly simplifying the algorithm.Numerical results show that the method is effective.