A projective averaged Kaczmarz iteration for nonlinear ill-posed problems
A projective averaged Kaczmarz iteration for nonlinear ill-posed problems
复制标题
非线性不适定问题的投影平均 Kaczmarz 迭代
DOI：
10.1088/1361-6420/aba5ef
复制
发表时间：
2020
期刊：
影响因子：
2.1
通讯作者：
Tang Jinping
中科院分区：
文献类型：
--
作者：
Tong Shanshan;Han Bo;Tang Jinping
平均Kaczmarz迭代法是Landweber法和Kaczmarz法的一种混合算法，它具有易于实现和提高稳定性的优点，适用于求解多个非线性方程组。本文通过引入同伦扰动Kaczmarz的搜索方向和一个投影策略，提出了一种加速平均Kaczmarz型迭代方法。通过使用中间变量的平均值来更新新的变量。这些变量是由以前的迭代到条纹的度量投影得到的，它与前向算子的性质和噪声水平有关。在与Landweber Kaczmarz方法类似的假设下，我们给出了该方法的收敛性分析。参数识别问题的数值实验验证了该方法具有明显的加速效果和重构稳定性。
The averaged Kaczmarz iteration is a hybrid of the Landweber method and Kaczmarz method with easy implementation and increased stability for solving problems with multi nonlinear equations. In this paper, we propose an accelerated averaged Kaczmarz type iterative method by introducing the search direction of homotopy perturbation Kaczmarz and a projective strategy. The new iterate is updated by using an average over the intermediate variables. These variables are obtained by the metric projection of previous iterates onto the stripes which are related to the property of forward operator and noise level. We present the convergence analysis of the proposed method under the similar assumptions of Landweber Kaczmarz method. The numerical experiments on parameter identification problem validate that the proposed method has evident acceleration effect and reconstruction stability.