Computing the Structured Pseudospectrum of a Toeplitz Matrix and Its Extreme Points
Computing the Structured Pseudospectrum of a Toeplitz Matrix and Its Extreme Points
复制标题
计算托普利茨矩阵的结构化伪谱及其极值点
DOI：
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发表时间：
2012
影响因子：
1.5
通讯作者：
Silvia Noschese
中科院分区：
文献类型：
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作者：
P. Buttà;Nicola Guglielmi;Silvia Noschese
讨论了Toeplitz矩阵的结构化伪谱横坐标和半径（关于Frobenius范数）的计算，并给出了两种基于低秩性质构造极值扰动的算法.这些算法受到[N. Guglielmi和M. Overton，SIAM J. Matrix Anal.应用程序、32（2011），pp. 1166--1192]，但将它们推广到结构伪谱和分析中存在一些困难。自然概括的算法，使我们能够绘制显着的部分结构的pseudospectrum在极值点附近，也进行了讨论。由于没有算法在文献中绘制这样的结构化伪谱，我们提出的方法似乎有希望扩展现有的软件工具（Eigtool，Seigtool）的Toeplitz矩阵的结构化伪谱表示。我们讨论了算法的局部收敛性质，并给出了一些应用实例。
The computation of the structured pseudospectral abscissa and radius (with respect to the Frobenius norm) of a Toeplitz matrix is discussed and two algorithms based on a low-rank property to construct extremal perturbations are presented. The algorithms are inspired by those considered in [N. Guglielmi and M. Overton, SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166--1192] for the unstructured case, but their extension to structured pseudospectra and analysis presents several difficulties. Natural generalizations of the algorithms, allowing us to draw significant sections of the structured pseudospectra in proximity of extremal points, are also discussed. Since no algorithms are available in the literature to draw such structured pseudospectra, the approach we present seems promising to extend existing software tools (Eigtool, Seigtool) to structured pseudospectra representation for Toeplitz matrices. We discuss local convergence properties of the algorithms and show some applications to a few illustrative...