Condition numbers for the nonlinear matrix equation and their statistical estimation
Condition numbers for the nonlinear matrix equation and their statistical estimation
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DOI：
10.1016/j.laa.2015.06.011
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发表时间：
2015-10
影响因子：
1.1
通讯作者：
Shaoxin Wang;Hu Yang;Hanyu Li
中科院分区：
文献类型：
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作者：
Shaoxin Wang;Hu Yang;Hanyu Li
本文考虑了非线性矩阵方程X+ A - F (X) A= Q的四种不同类型的条件数，即两种正态条件数，混合条件数和成分条件数，并推导了它们的显式表达式。利用概率谱范数估计和统计条件估计方法，可以较好地估计出这些条件数。给出了两个数值算例，分别说明了正态条件数与混合条件数和成分条件数的区别，以及估计器的效率。
In this paper, we consider four different types of condition numbers, ie, two normwise ones, mixed and componentwise ones, for the nonlinear matrix equation X+ A⋆ F (X) A= Q, and derive their explicit expressions. Using the probabilistic spectral norm estimator and the statistical condition estimation method, these condition numbers can be estimated with high reliability. Two numerical examples are provided to illustrate the difference between the normwise condition numbers and the mixed and componentwise condition numbers, and the efficiency of the estimators, respectively.