论文标题
在非组织迭代的Tikhonov方法中选择Lagrange乘数的范围重复标准
Range-relaxed criteria for choosing the Lagrange multipliers in nonstationary iterated Tikhonov method
论文作者
论文摘要
在本文中，我们提出了一种新型的非平稳迭代tikhonov（NIT）类型方法，用于获得稳定的近似解决方案，以通过在希尔伯特空间之间作用的线性操作员建模的不足的操作员方程。该问题的几何特性用于得出一个新的策略，以选择NIT迭代的正则化参数序列（Lagrange乘数）。提供了这种新方法的收敛分析。为两个不同的应用提供了数值实验：i）2D椭圆参数识别问题（反向电位问题）； ii）图像过度问题。获得的结果验证了我们方法的效率与NIT方法的标准实现相比（其中通常用于Lagrange乘数序列的几何选择）。
In this article we propose a novel nonstationary iterated Tikhonov (NIT) type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical properties of the problem are used to derive a new strategy for choosing the sequence of regularization parameters (Lagrange multipliers) for the NIT iteration. Convergence analysis for this new method is provided. Numerical experiments are presented for two distinct applications: I) A 2D elliptic parameter identification problem (Inverse Potential Problem); II) An image deblurring problem. The results obtained validate the efficiency of our method compared with standard implementations of the NIT method (where a geometrical choice is typically used for the sequence of Lagrange multipliers).
