Absolute and relative Weyl theorems for generalized eigenvalue problems
Absolute and relative Weyl theorems for generalized eigenvalue problems
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DOI：
10.1016/j.laa.2009.08.001
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发表时间：
2010
影响因子：
1.1
通讯作者：
Y. Nakatsukasa
中科院分区：
文献类型：
--
作者：
Y. Nakatsukasa
导出了Hermitian定束A-λB的Weyl型特征值微扰理论，其中B是正定的.结果提供了一个原始和扰动特征值之间的一一对应，并给出了一个统一的扰动界。我们给出了绝对和相对扰动的结果，定义在标准的欧几里德度量，而不是弦度量，经常使用。
Weyl-type eigenvalue perturbation theories are derived for Hermitian definite pencils A-λB, in which B is positive definite. The results provide a one-to-one correspondence between the original and perturbed eigenvalues, and give a uniform perturbation bound. We give both absolute and relative perturbation results, defined in the standard Euclidean metric instead of the chordal metric that is often used.