Results 1  10
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19
On the Sensitivity of the SR Decomposition
, 1992
"... Firstorder componentwise and normwise perturbation bounds for the SR decomposition are presented. The new normwise bounds are at least as good as previous known results. In particular, for the R factor, the normwise bound can be significantly tighter than the previous result. 1. ..."
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Firstorder componentwise and normwise perturbation bounds for the SR decomposition are presented. The new normwise bounds are at least as good as previous known results. In particular, for the R factor, the normwise bound can be significantly tighter than the previous result. 1.
A Perturbation Analysis for R in the QR Factorization
 In preparation
, 1995
"... We present new normwise and componentwise perturbation analyses for the R factor of the QR factorization A = Q1R of an m \Theta n matrix A with full column rank. The analyses more accurately reflect the sensitivity of the problem than previous normwise and componentwise results. The new condition nu ..."
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Cited by 8 (6 self)
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We present new normwise and componentwise perturbation analyses for the R factor of the QR factorization A = Q1R of an m \Theta n matrix A with full column rank. The analyses more accurately reflect the sensitivity of the problem than previous normwise and componentwise results. The new condition
New Methods for Estimating the Distance to Uncontrollability
, 1999
"... Controllability is a fundamental concept in control theory. Given a linear control system, we present new algorithms for estimating its distance to uncontrollability, i.e., the norm of the normwise smallest perturbation that makes the given system uncontrollable. Many algorithms have been previousl ..."
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Cited by 22 (2 self)
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Controllability is a fundamental concept in control theory. Given a linear control system, we present new algorithms for estimating its distance to uncontrollability, i.e., the norm of the normwise smallest perturbation that makes the given system uncontrollable. Many algorithms have been
Error bounds from extra precise iterative refinement
 ACM Transactions on Mathematical Software
, 2006
"... We present the design and testing of an algorithm for iterative refinement of the solution of linear equations, where the residual is computed with extra precision. This algorithm was originally proposed in the 1960s [6, 22] as a means to compute very accurate solutions to all but the most illcondi ..."
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Cited by 36 (5 self)
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for the computed solution. The completion of the new BLAS Technical Forum Standard [5] has recently removed the first obstacle. To overcome the second obstacle, we show how a single application of iterative refinement can be used to compute an error bound in any norm at small cost, and use this to compute both
New Perturbation Analyses For The Cholesky Factorization
, 1995
"... this paper is to establish new first order bounds on the norm of the perturbation in the Cholesky factor, sharper than that of Sun (1991) and Stewart (1993). Also, we obtain a new first order bound for the components of the perturbation, and give strict bounds on the norm and components of the pertu ..."
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Cited by 9 (7 self)
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this paper is to establish new first order bounds on the norm of the perturbation in the Cholesky factor, sharper than that of Sun (1991) and Stewart (1993). Also, we obtain a new first order bound for the components of the perturbation, and give strict bounds on the norm and components
Rigorous perturbation bounds for some matrix factorizations
 SIAM J. Matrix Anal. Appl
"... Abstract. 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 algor ..."
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Cited by 6 (3 self)
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Abstract. 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
Robust H∞ observer design for a class of nonlinear uncertain systems via convex optimization
 Proceedings of the 2007 American Control Conference
"... AbstractA new approach of robust H∞ observer design for a class of Lipschitz nonlinear systems with timevarying uncertainties is proposed in the LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiob ..."
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Cited by 8 (3 self)
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AbstractA new approach of robust H∞ observer design for a class of Lipschitz nonlinear systems with timevarying uncertainties is proposed in the LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex
The Arnoldi method in the light of Homotopic Deviation theory
, 2003
"... This paper aims at providing an algorithmic understanding of the “convergence” of Krylovtype methods which relies on asymptotic properties at 0 and ∞. The classical normwise (or analytic) perturbation approach correponds to the limit towards 0. We complement this analysis by the structural perturba ..."
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Cited by 3 (3 self)
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This paper aims at providing an algorithmic understanding of the “convergence” of Krylovtype methods which relies on asymptotic properties at 0 and ∞. The classical normwise (or analytic) perturbation approach correponds to the limit towards 0. We complement this analysis by the structural
A Statistical Analysis of the Numerical Condition of Multiple Roots of Polynomials
, 2003
"... Componentwise and normwise condition numbers of an m{tuple root x 0 of a polynomial p(x) that are appropriate for measurement and experimental inaccuracies are derived. These new condition numbers must be compared with the established condition numbers, which are appropriate for quantifying the ..."
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Cited by 3 (3 self)
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Componentwise and normwise condition numbers of an m{tuple root x 0 of a polynomial p(x) that are appropriate for measurement and experimental inaccuracies are derived. These new condition numbers must be compared with the established condition numbers, which are appropriate for quantifying
Integer DCTII by Lifting Steps
 IN: ADVANCES IN MULTIVARIATE APPROXIMATION
, 2002
"... In image compression, the discrete cosine transform of type II (DCTII) is of special interest. In this paper we use a new approach to construct an integer DCTII first considered in [14]. Our method is based on a factorization of the cosine matrix of type II into a product of sparse, orthogonal mat ..."
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Cited by 2 (1 self)
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In image compression, the discrete cosine transform of type II (DCTII) is of special interest. In this paper we use a new approach to construct an integer DCTII first considered in [14]. Our method is based on a factorization of the cosine matrix of type II into a product of sparse, orthogonal
Results 1  10
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19