摘要
利用Landweber-Kaczmarz迭代算法研究非线性不适定问题.首先,在Banach空间引入Bregman距离,构造合适的步长,说明Bregman距离序列在迭代算法中是单调递减的.然后,由凸分析、对偶映射和Fréchet可微的性质得到迭代算法具有收敛性.
In this paper, we study the Landweber-Kaczmarz iterative algorithm for nonlinear ill-posed problems. We first introduce the iterative step, and then derive the sequence of Bregman distance which is monotonously decreasing in Banach space. With the convex analysis, duality mapping and Fréchet differentiable, we succeed in obtaining the convergence of the iterative algorithm.
引文
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