交替分离算法的基础理论分析

对交替分离算法与交替投影算法作了如下几方面比较对应多维优化问题有关波形变量的拟合差异;对应算子方程线性与非线性差异;对应一维优化问题外形完全一致,但拟合矢量的线性与非线性差异;对应一维拟合矢量对当前估计参数的依赖与非依赖差异;对应多维优化问题目标函数光滑与非光滑差异,及一维优化问题目标函数连续与非连续差异.从较深的理论层次对算法的稳健性问题作了初步探讨.对部分结论作了计算机模拟.

The Basic Theory Analysis of Alternating Separation Algorithm

This paper compares the alternating separation (AS) algorithm with the alternating projection (AP) algorithm in different aspects, such as, the difference of solving the waveform variable, the linearity and non-linearity of the operator equation and of one-dimensional fitting vector, the difference of the fitting vector dependent or independent of the current estimation of the interesting parameter, the smooth or non-continuous of the objective function of the AS and AP. Finally, an initial research is made on the robustness of the algorithms with the view of theory, computer simulations confirm some theory conclusions.