Approximated structured pseudospectra
Approximated structured pseudospectra
复制标题
近似结构化赝谱
DOI：
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发表时间：
2016
影响因子：
4.3
通讯作者：
L. Reichel
中科院分区：
文献类型：
--
作者：
S. Noschese;L. Reichel
伪谱和结构伪谱是分析矩阵的重要工具。然而，它们的计算对于除了小矩阵之外的所有矩阵来说都是非常苛刻的。提出了一种计算伪谱和结构伪谱近似的新方法，该方法基于确定给定矩阵的许多适当选择的秩一或投影秩一扰动的谱。选择秩一或投影秩一扰动的灵感来自威尔金森对特征值敏感性的分析。数值算例表明，该方法比随机或结构化随机秩一扰动能更好地理解伪谱和结构化伪谱，且计算量更小。后一种方法是目前常用的结构伪光谱的测定方法。
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and structured pseudospectra, based on determining the spectra of many suitably chosen rank‐one or projected rank‐one perturbations of the given matrix is proposed. The choice of rank‐one or projected rank‐one perturbations is inspired by Wilkinson's analysis of eigenvalue sensitivity. Numerical examples illustrate that the proposed approach gives much better insight into the pseudospectra and structured pseudospectra than random or structured random rank‐one perturbations with lower computational burden. The latter approach is presently commonly used for the determination of structured pseudospectra.