基于自适应BB步长的修正Landweber迭代算法及收敛性分析

Modified Landweber Iterative Algorithm Based on Adaptive BB Step Size and Its Convergence Analysis

Landweber迭代法是求解数学物理反问题的一种重要方法,其具有良好的稳定性。然而,Landweber迭代正则化方法收敛速度相对较慢,限制了其在现实问题中的广泛应用。本文基于Landweber迭代正则化方法,引入自适应Barzilai-Borwein (ABB)步长加速技巧,提出了加速的Landweber迭代正则化方法,并给出了方法的收敛性分析。基于椭圆方程约束的参数识别问题,从数值计算角度验证了方法的有效性。实验结果表明相对于Landweber迭代方法,本文提出的Landweber-ABB迭代正则化方法在收敛速度方面具有较好的优势。

Landweber iterative method is an important method for solving inverse problems in mathematical physics, which has good stability. However, the convergence speed of Landweber iterative regularization method is relatively slow, which limits its wide application in practical problems. Based on the Landweber iterative regularization method, this paper proposes an accelerated Landweber iterative regularization method by introducing adaptive Barzilai-Borwein (ABB) step acceleration technique and gives the convergence analysis of the method. Based on the parameter identification problem constrained by elliptic equation, the effectiveness of the method is verified from the perspective of numerical calculation. The experimental results demonstrate that the Landweber-ABB iterative regularization method proposed in this paper has better convergence speed than the Landweber iterative method.