Cubically convergent methods for selecting the regularization parameters in linear inverse problems
Cubically convergent methods for selecting the regularization parameters in linear inverse problems
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DOI：
10.1016/j.jmaa.2009.03.024
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发表时间：
2009-08
影响因子：
1.3
通讯作者：
Yongkui Zou;Linjun Wang;Ran Zhang
中科院分区：
文献类型：
--
作者：
Yongkui Zou;Linjun Wang;Ran Zhang
给出了三种三次收敛的线性反问题正则化参数选取方法。给出了具体的算法，并估计了收敛速度.我们的基本工具是Tikhonov正则化和Morozov的差异原则。我们证明了与标准Newton方法相比，我们的三次收敛方法的计算量几乎相同，但迭代步数更少，并通过一个椭圆边值问题的数值实验验证了所提算法的有效性.
We present three cubically convergent methods for choosing the regularization parameters in linear inverse problems. The detailed algorithms are given and the convergence rates are estimated. Our basic tools are Tikhonov regularization and Morozov's discrepancy principle. We prove that, in comparison with the standard Newton method, the computational costs for our cubically convergent methods are nearly the same, but the number of iteration steps is even less. Numerical experiments for an elliptic boundary value problem illustrate the efficiency of the proposed algorithms.