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281,709
Perturbation Bounds For The Polar Decomposition
, 1997
"... . Let Mn (F ) denote the space of matrices over the field F . Given A2 Mn (F ) define jAj j (A A) 1=2 and U (A) j AjAj \Gamma1 assuming A is nonsingular. Let oe 1 (A) oe 2 (A) \Delta \Delta \Delta oe n (A) 0 denote the ordered singular values of A. We obtain majorization results relating ..."
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Cited by 22 (3 self)
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. Let Mn (F ) denote the space of matrices over the field F . Given A2 Mn (F ) define jAj j (A A) 1=2 and U (A) j AjAj \Gamma1 assuming A is nonsingular. Let oe 1 (A) oe 2 (A) \Delta \Delta \Delta oe n (A) 0 denote the ordered singular values of A. We obtain majorization results relating the singular values of U (A + \DeltaA) \Gamma U (A) and those of A and \DeltaA. In particular we show that if A; \DeltaA2 Mn (R) and oe 1 (\DeltaA) ! oe n (A) then for any unitarily invariant norm k \Delta k, kU (A + \DeltaA) \Gamma U (A)k 2[oe n\Gamma1 (A) + oe n (A)] \Gamma1 k\DeltaAk. We obtain similar results for matrices with complex entries. We also consider the unitary Procrustes problem: minfkA \Gamma UBk : U2 Mn (C); U U = Ig where A; B2 Mn (C) and a unitarily invariant norm k \Delta k are given. It was conjectured that if U is unitary and U BA is positive semidefinite then U must be a solution to the unitary Procrustes problem for all unitarily invariant norms. We sh...
Maximal unidirectional perturbation bounds
, 1988
"... for stability of polynomials and matrices * ..."
Perturbation Bounds for Hyperbolic Matrix Factorizations
, 2005
"... 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, � J)orthogonal factors, that is, matrices that satisfy H T JH = � J,whereJand � J are diagonal with diagonal element ..."
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elements ±1. The purpose of this work is to analyze the perturbation of matrix factorizations that have a (J, � J)orthogonal or orthogonal factor and to give first order perturbation bounds. For each factorization analyzed, we give the sharpest possible first order bound, which yields a condition number
Estimation of Perturbation Bounds for Finite Trajectories
, 2000
"... The problem of estimating perturbation bounds for finite trajectories of nonautonomous systems is considered. A worst case sensitivity derivative of the trajectory with respect to the uncertainty is used to verify that the perturbed trajectory is within a given neighborhood of the nominal. This giv ..."
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The problem of estimating perturbation bounds for finite trajectories of nonautonomous systems is considered. A worst case sensitivity derivative of the trajectory with respect to the uncertainty is used to verify that the perturbed trajectory is within a given neighborhood of the nominal
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 906 (36 self)
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the variation in the perturbed quantity. Up to the higherorder terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares
THE OPTIMAL PERTURBATION BOUNDS FOR THE WEIGHTED MOOREPENROSE INVERSE ∗
"... Abstract. In this paper, we obtain optimal perturbation bounds of the weighted MoorePenrose inverse under the weighted unitary invariant norm, the weighted Qnorm and the weighted Fnorm, and thereby extend some recent results. ..."
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Abstract. In this paper, we obtain optimal perturbation bounds of the weighted MoorePenrose inverse under the weighted unitary invariant norm, the weighted Qnorm and the weighted Fnorm, and thereby extend some recent results.
Comparison of perturbation bounds for the stationary distribution of a Markov chain
 IN PROCEEDINGS OF THE TWENTYSIXTH INTERNATIONAL CONFERENCE ON VERY LARGE DATABASES
, 2000
"... The purpose of this paper is to review and compare the existing perturbation bounds for the stationary distribution of a finite, irreducible, homogeneous Markov chain. ..."
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Cited by 66 (2 self)
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The purpose of this paper is to review and compare the existing perturbation bounds for the stationary distribution of a finite, irreducible, homogeneous Markov chain.
Spectral perturbation bounds for selfadjoint operators I ∗
, 704
"... We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudoFrierdrichs extension. We also give several generalisations of the aforementioned extension. 1 ..."
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We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudoFrierdrichs extension. We also give several generalisations of the aforementioned extension. 1
Results 1  10
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281,709