A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
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矩阵微扰理论的几何方法和矩阵铅笔。
DOI：
10.1137/s0895479895284634
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
B. Kågström
中科院分区：
文献类型：
--
作者：
A. Edelman;E. Elmroth;B. Kågström
通过导出严格等价矩阵束轨道的法空间的切空间和正交基，我们导出了Kronecker标准形的非线性变形。这些变形揭示了与Kronecker标准形有关的矩阵束的局部微扰理论。我们还得到了一个新的奇异值界的距离较低的一般铅笔的轨道。文中的概念、结果及其推导主要用数值线性代数的语言来表达。我们的结论与实验和应用。
We derive versal deformations of the Kronecker canonical form by deriving the tangent space and orthogonal bases for the normal space to the orbits of strictly equivalent matrix pencils. These deformations reveal the local perturbation theory of matrix pencils related to the Kronecker canonical form. We also obtain a new singular value bound for the distance to the orbits of less generic pencils. The concepts, results, and their derivations are mainly expressed in the language of numerical linear algebra. We conclude with experiments and applications.