Some Regularity Results for the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix
نویسندگان
چکیده
منابع مشابه
Some Regularity Results for the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix
The ε-pseudospectral abscissa αε and radius ρε of an n× n matrix are, respectively, the maximal real part and the maximal modulus of points in its ε-pseudospectrum, defined using the spectral norm. It was proved in [A.S. Lewis and C.H.J. Pang, SIAM J. Optim., 19 (2008), pp. 1048–1072] that for fixed ε > 0, αε and ρε are Lipschitz continuous at a matrix A except when αε and ρε are attained at a ...
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The ε-pseudospectral abscissa and radius of an n × n matrix are respectively the maximal real part and the maximal modulus of points in its ε-pseudospectrum, defined using the spectral norm. Existing techniques compute these quantities accurately but the cost is multiple singular value decompositions and eigenvalue decompositions of order n, making them impractical when n is large. We present n...
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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 fo...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2012
ISSN: 1052-6234,1095-7189
DOI: 10.1137/110822840