ANALYSIS OF DISCRETE ILL-POSED PROBLEMS BY MEANS OF THE L-CURVE
ANALYSIS OF DISCRETE ILL-POSED PROBLEMS BY MEANS OF THE L-CURVE
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DOI：
10.1137/1034115
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发表时间：
1992-12-01
期刊：
影响因子：
10.2
通讯作者：
HANSEN, PC
中科院分区：
文献类型：
--
作者：
HANSEN, PC
当用各种数值正则化技术分析和求解离散不适定问题时，显示正则解的信息的一个非常方便的方法是绘制解的范数或半范数相对于残差向量的范数。特别是，与Tikhonov正则化相关的图起着核心作用。本文的主要目的是提倡在离散不适定问题的数值处理中使用该图。对图进行了定量刻画，得到了正则解与图之间的几个重要关系。文中还证明了几种选择正则化参数的方法与定位图的特征L形“角”有关。
When discrete ill-posed problems are analyzed and solved by various numerical regularization techniques, a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector. In particular, the graph associated with Tikhonov regularization plays a central role. The main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill-posed problems. The graph is characterized quantitatively, and several important relations between regularized solutions and the graph are derived. It is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic L-shaped "corner" of the graph.