EIGENVALUES, PSEUDOSPECTRUM AND STRUCTURED PERTURBATIONS
EIGENVALUES, PSEUDOSPECTRUM AND STRUCTURED PERTURBATIONS
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DOI：
10.1016/j.laa.2005.06.009
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发表时间：
2006-03
影响因子：
1.1
通讯作者：
S. Rump
中科院分区：
文献类型：
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作者：
S. Rump
研究了结构扰动下特征值的行为。我们证明了许多常见的结构，如（复）对称，Toeplitz，对称Toeplitz，循环和其他的结构条件数是等于非结构条件数的normwise扰动，并证明了类似的结果真实的扰动。一个例外是复杂的反对称矩阵。我们还研究了分量复扰动和真实的扰动。这里厄米特矩阵和斜厄米特矩阵对于真实的扰动是例外的。此外，我们的结构化（复杂的和真实的）的伪谱的一些结构，并表明，往往有很少或没有显着的差异，通常的，非结构化的伪谱。
We investigate the behavior of eigenvalues under structured perturbations. We show that for many common structures such as (complex) symmetric, Toeplitz, symmetric Toeplitz, circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations, and prove similar results for real perturbations. An exception are complex skewsymmetric matrices. We also investigate componentwise complex and real perturbations. Here Hermitian and skew-Hermitian matrices are exceptional for real perturbations. Furthermore we characterize the structured (complex and real) pseudospectrum for a number of structures and show that often there is little or no significant difference to the usual, unstructured pseudospectrum.