Perturbation bounds for the operator absolute value
نویسندگان
چکیده
منابع مشابه
Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds
We show that three well-known perturbation bounds for matrix eigenvalues imply relative bounds: the Bauer-Fike and Hooman-Wielandt theorems for diagonalisable matrices, and Weyl's theorem for Hermitian matrices. As a consequence, relative perturbation bounds are not necessarily stronger than absolute bounds; and the conditioning of an eigenvalue in the relative sense is the same as in the absol...
متن کاملRelative and Absolute Perturbation Bounds for Weighted Polar Decomposition
Let Cm×n, Cm×n r , C m ≥ , C m > , and In denote the set of m × n complex matrices, subset of Cm×n consisting of matrices with rank r, set of the Hermitian nonnegative definite matrices of order m, subset of C ≥ consisting of positive-definite matrices and n × n unit matrix, respectively. Without specification, we always assume that m > n >max{r, s} and the given weight matrices M ∈ C > ,N ∈ C ...
متن کاملPerturbation bounds for $g$-inverses with respect to the unitarily invariant norm
Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...
متن کاملLower Bounds for the Absolute Value of Random Polynomials on a Neighborhood of the Unit Circle
Let T (x) = Pn−1 j=0 ±eijx where ± stands for a random choice of sign with equal probability. The first author recently showed that for any � > 0 and most choices of sign minx∈[0,2π) |T (x)| < n−1/2+� provided n is large. In this paper we show that the power n−1/2 is optimal. More precisely, for sufficiently small � > 0 and large n most choices of sign satisfy minx∈[0,2π) |T (x)| > �n−1/2. Furt...
متن کاملSpectral Perturbation Bounds for Positive
Let H and H + H be positive deenite matrices. It was shown by Barlow and Demmel, and Demmel and Veseli c that if one takes a component-wise approach one can prove much stronger bounds on i (H)== i (H++H) and the components of the eigenvectors of H and H++H than by using the standard norm-wise perturbation theory. Here a uniied approach is presented that improves on the results of Barlow, Demmel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00201-2