论文标题
关于求解非线性不良方程式系统的投射Landweber-Kaczmarz方法
On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations
论文作者
论文摘要
在本文中，我们将作者最近提出的投影陆地方法与Kaczmarz解决非线性不良方程式系统的方法相结合。这项工作中使用的基本假设是切向锥条件。我们表明，提出的迭代是一种收敛的正则化方法。对与Dirichlet到Neumann Map相关的非线性逆问题进行了数值测试，这表明与其他良好建立的迭代相比，该方法的性能卓越。我们的初步研究表明，由此产生的迭代是计算非线性不良方程大规模系统稳定解决方案的有前途替代方法。
In this article we combine the projective Landweber method, recently proposed by the authors, with Kaczmarz's method for solving systems of non-linear ill-posed equations. The underlying assumption used in this work is the tangential cone condition. We show that the proposed iteration is a convergent regularization method. Numerical tests are presented for a non-linear inverse problem related to the Dirichlet-to-Neumann map, indicating a superior performance of the proposed method when compared with other well established iterations. Our preliminary investigation indicates that the resulting iteration is a promising alternative for computing stable solutions of large scale systems of nonlinear ill-posed equations.
