Adaptive multilevel iteration methods for solving ill-posed integral equations via a coupled system
Adaptive multilevel iteration methods for solving ill-posed integral equations via a coupled system
复制标题
通过耦合系统求解不适定积分方程的自适应多级迭代方法
DOI：
10.1088/1361-6420/ac1361
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发表时间：
2021
期刊：
影响因子：
2.1
通讯作者：
Zhou Duanmei
中科院分区：
文献类型：
--
作者：
Zhang Rong;Luo Xingjun;Hu Wenyu;Zhou Duanmei
提出了一种通过耦合系统的自适应多级迭代方法，从而产生快速有效的算法来求解不适定积分方程。该算法可以自适应地选择离散层和迭代次数。通过施加投影条件，在一定的源条件下建立了该算法的先验参数选择规则和两个后验参数选择规则的收敛速度。数值结果分别说明了采用平衡原理和差异原理的自适应多级迭代方法的性能。
An adaptive multilevel iteration method via a coupled system is proposed, which leads to fast and effective algorithm for solving ill-posed integral equations. In this algorithm, the discrete layer and the iteration can be selected adaptively. By imposing projection conditions, convergence rates of an a priori parameter choice rule and two a posteriori parameter choice rule for this algorithm are established under certain source conditions. Numerical results are presented to illustrate the performance of adaptive multilevel iteration methods with the balance principle and the discrepancy principle, respectively.