Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem
Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem
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DOI：
10.1109/cdc.2015.7402875
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Jackeline Abad Torres;Sandip Roy
中科院分区：
文献类型：
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作者：
Jackeline Abad Torres;Sandip Roy
我们研究了一个本质非负矩阵的主特征值的最小化问题，相对于一个保迹或固定迹对角扰动，在这种情况下，只有一个子集的对角条目可以被扰动。在最佳的扰动矩阵的频谱的特点。一个建设性的算法计算最佳对角保迹扰动的发展，使用谱结果与线和对称化参数。一些图论的结果开发的最佳扰动和它如何变化，如果进一步的条目受到约束，部分使用的性质的Perron补的非负矩阵。
We study the problem of minimizing the dominant eigenvalue of an essentially-nonnegative matrix with respect to a trace-preserving or fixed-trace diagonal perturbation, in the case where only a subset of the diagonal entries can be perturbed. The spectrum of the perturbed matrix at the optimum is characterized. A constructive algorithm for computing the optimal diagonal trace-preserving perturbation is developed, using the spectral result together with line-sum-symmetrization arguments. A number of graph-theoretic results are developed on the optimal perturbation and how it changes if further entries are constrained, in part using properties of the Perron complement of nonnegative matrices.