Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
نویسندگان
چکیده
منابع مشابه
Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations∗
The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are...
متن کاملRelative Perturbation Theory: (I) Eigenvalue Variations
In this paper, we consider how eigenvalues of a matrix A change when it is perturbed to e A = D 1AD2 and how singular values of a (nonsquare) matrix B change when it is perturbed to e B = D 1BD2, where D1 and D2 are assumed to be close to unitary matrices of suitable dimensions. We have been able to generalize many well-known perturbation theorems, including Ho man-Wielandt theorem and Weyl-Lid...
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The classical perturbation theory for Hermitian matrix eigenvalue and singular value problems provides bounds on invariant subspace variations that are proportional to the reciprocals of absolute gaps between subsets of spectra or subsets of singular values. These bounds may be bad news for invariant subspaces corresponding to clustered eigenvalues or clustered singular values of much smaller m...
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v Acknowledgments vi Chapter
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When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 1998
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s089547989629849x