Algorithms for the computation of the pseudospectral radius and the numerical radius of a matrix
Algorithms for the computation of the pseudospectral radius and the numerical radius of a matrix
复制标题
计算矩阵的伪谱半径和数值半径的算法
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
M. Overton
中科院分区：
文献类型：
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作者：
E. Mengi;M. Overton
离散时间动力系统xk+1 = Axk的鲁棒稳定性的两个有用度量是A的拟谱半径和数值半径。A的伪谱半径是A的伪谱中的点的模的最大值，而数值半径是值域中的点的模的最大值。我们提出了一种计算拟谱半径和数值半径的全局收敛算法.对于前一种算法，我们讨论了它是二次收敛的条件，并提供了详细的精度分析，给出了算法是向后稳定的条件。该算法的灵感来自Byers，Boyd-Balakrishnan，He-Watson和Burke-Lewis-Overton的相关问题的方法，并依赖于计算辛束和Hamilton矩阵的特征值。
Two useful measures of the robust stability of the discrete-time dynamical system xk+1 = Axk are the � -pseudospectral radius and the numerical radius of A. The � -pseudospectral radius of A is the largest of the moduli of the points in the � -pseudospectrum of A, while the numerical radius is the largest of the moduli of the points in the field of values. We present globally convergent algorithms for computing the � -pseudospectral radius and the numerical radius. For the former algorithm, we discuss conditions under which it is quadratically convergent and provide a detailed accuracy analysis giving conditions under which the algorithm is backward stable. The algorithms are inspired by methods of Byers, Boyd– Balakrishnan, He–Watson and Burke–Lewis–Overton for related problems and depend on computing eigenvalues of symplectic pencils and Hamiltonian matrices.