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Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems
SIAM Journal on Matrix Analysis and Applications ( IF 1.5 ) Pub Date : 2021-01-01 , DOI: 10.1137/20m1344184
Volker Mehrmann , Paul Van Dooren

When computing the eigenstructure of matrix pencils associated with the passivity analysis of perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that the computed spectrum satisfies the symmetries that corresponds to this structure and the underlying physical system. We perform a backward error analysis and show that for matrix pencils associated with port-Hamiltonian descriptor systems and a given computed eigenstructure with the correct symmetry structure there always exists a nearby port-Hamiltonian descriptor system with exactly that eigenstructure. We also derive bounds for how near this system is and show that the stability radius of the system plays a role in that bound.

中文翻译:

线性 Port-Hamiltonian 描述符系统特征值的结构化后向误差

当使用结构化广义特征值方法计算与扰动端口-汉密尔顿描述符系统的被动分析相关的矩阵铅笔的特征结构时,应确保计算的频谱满足与该结构和底层物理系统相对应的对称性。我们执行后向误差分析并表明,对于与端口-哈密尔顿描述符系统相关的矩阵铅笔和具有正确对称结构的给定计算特征结构,总是存在附近的端口-汉密尔顿描述符系统,该系统恰好具有该特征结构。我们还推导出该系统与该系统的接近程度的界限,并表明该系统的稳定半径在该界限中起作用。
更新日期:2021-01-01
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