On Pseudospectra, Critical Points, and Multiple Eigenvalues of Matrix Pencils
On Pseudospectra, Critical Points, and Multiple Eigenvalues of Matrix Pencils
复制标题
关于矩阵铅笔的伪谱、临界点和多重特征值
DOI：
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发表时间：
2010
影响因子：
1.5
通讯作者：
R. Byers
中科院分区：
文献类型：
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作者：
Sk. Safique Ahmad;R. Alam;R. Byers
我们建立了一个定义和分析矩阵铅笔伪谱的通用框架。这样开发的框架统一了文献中提出的矩阵铅笔伪谱的各种定义。引入并分析了矩阵铅笔近似特征值的向后误差临界点，证明了每个临界点都是适当扰动的铅笔的多重特征值。证明了矩阵束的伪谱分支的公共边界点是临界点。特别地，我们证明了极小临界点可以从矩阵铅笔的伪谱中读出。因此，我们证明了关于矩阵束的Wilkinson问题的解可以从矩阵束的伪谱中读出。
We develop a general framework for defining and analyzing pseudospectra of matrix pencils. The framework so developed unifies various definitions of pseudospectra of matrix pencils proposed in the literature. We introduce and analyze critical points of backward errors of approximate eigenvalues of matrix pencils and show that each critical point is a multiple eigenvalue of an appropriately perturbed pencil. We show that common boundary points of components of pseudospectra of a matrix pencil are critical points. In particular, we show that a minimal critical point can be read off from the pseudospectra of matrix pencils. Hence we show that a solution of Wilkinson's problem for a matrix pencil can be read off from the pseudospectra of the matrix pencil.