Perturbation bounds for matrix functions
نویسندگان
چکیده
منابع مشابه
Perturbation Bounds for Hyperbolic Matrix Factorizations
Several matrix factorizations depend on orthogonal factors, matrices that preserve the Euclidean scalar product. Some of these factorizations can be extended and generalized to (J, J̃)-orthogonal factors, that is, matrices that satisfy H JH = J̃ , where J and J̃ are diagonal with diagonal elements ±1. The purpose of this work is to analyze the perturbation of matrix factorizations that have a (J, ...
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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 کاملRigorous Perturbation Bounds of Some Matrix Factorizations
This article presents rigorous normwise perturbation bounds for the Cholesky, LU and QR factorizations with normwise or componentwise perturbations in the given matrix. The considered componentwise perturbations have the form of backward rounding errors for the standard factorization algorithms. The used approach is a combination of the classic and refined matrix equation approaches. Each of th...
متن کاملExamples of Perturbation Bounds of P-matrix Linear Complementarity Problems1
We use the semi-smooth Newton method [13] to solve (1.8) in [CX] with stop criteria kr(x)k ≤ 10−14 and computer precisionmacheps = 10−16. We report numerical results in Table 1 and Table 2 where the fourth column and the fifth column represent the measure β(M)kMk for the LCP and the upper bounds (4.5), (4.6) of K(M) for the system of (1.8) in [CX], respectively. An exact error k4xk is computed ...
متن کاملPerturbation Bounds of P-Matrix Linear Complementarity Problems
We define a new fundamental constant associated with a P-matrix and show that this constant has various useful properties for the P-matrix linear complementarity problems (LCP). In particular, this constant is sharper than the Mathias-Pang constant in deriving perturbation bounds for the P-matrix LCP. Moreover, this new constant defines a measure of sensitivity of the solution of the P-matrix L...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2020
ISSN: 1331-4343
DOI: 10.7153/mia-2020-23-84