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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
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.
Perturbation Analyses for the QR Factorization
 SIAM J. Matrix Anal. Appl
, 1997
"... This paper gives perturbation analyses for Q 1 and R in the QR factorization A = Q 1 R, Q T 1 Q 1 = I, for a given real m \Theta n matrix A of rank n. The analyses more accurately reflect the sensitivity of the problem than previous normwise results. The condition numbers here are altered by any c ..."
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Cited by 20 (11 self)
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This paper gives perturbation analyses for Q 1 and R in the QR factorization A = Q 1 R, Q T 1 Q 1 = I, for a given real m \Theta n matrix A of rank n. The analyses more accurately reflect the sensitivity of the problem than previous normwise results. The condition numbers here are altered by any
AND
, 1995
"... We present new perturbation analyses, for the Cholesky factorization A = RJR of a symmetric positive definite matrix A. The analyses more accurately reflect the sensitivity of the problem than previous normwise results. The condition numbers here are altered by any symmetric pivoting used in PAP1 = ..."
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We present new perturbation analyses, for the Cholesky factorization A = RJR of a symmetric positive definite matrix A. The analyses more accurately reflect the sensitivity of the problem than previous normwise results. The condition numbers here are altered by any symmetric pivoting used in PAP1
ON CONDITION NUMBERS FOR THE CANONICAL GENERALIZED POLAR DECOMPOSITION OF REAL MATRICES
, 2013
"... Three different kinds of condition numbers: normwise, mixed and componentwise, are discussed for the canonical generalized polar decomposition (CGPD) of real matrices. The technique used herein is different from the ones in previous literatures of the polar decomposition. With some modifications of ..."
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Three different kinds of condition numbers: normwise, mixed and componentwise, are discussed for the canonical generalized polar decomposition (CGPD) of real matrices. The technique used herein is different from the ones in previous literatures of the polar decomposition. With some modifications
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
k=0
"... Abstract. Component and normwise perturbation bounds for the block LU factorization and block LDL ∗ factorization of Hermitian matrices are presented. We also obtain, as a consequence, perturbation bounds for the usual pointwise LU, LDL∗, and Cholesky factorizations. Some of these latter bounds are ..."
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Abstract. Component and normwise perturbation bounds for the block LU factorization and block LDL ∗ factorization of Hermitian matrices are presented. We also obtain, as a consequence, perturbation bounds for the usual pointwise LU, LDL∗, and Cholesky factorizations. Some of these latter bounds
MONOTONICITY OF PERTURBED TRIDIAGONAL MMATRICES∗
"... Abstract. A wellknown property of anMmatrix is that its inverse is elementwise nonnegative, which we write as M−1 ≥ 0. In a previous paper [Linear Algebra Appl., 434 (2011), pp. 131–143], we gave sufficient bounds on single element perturbations so that monotonicity persists for a perturbed tridia ..."
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Abstract. A wellknown property of anMmatrix is that its inverse is elementwise nonnegative, which we write as M−1 ≥ 0. In a previous paper [Linear Algebra Appl., 434 (2011), pp. 131–143], we gave sufficient bounds on single element perturbations so that monotonicity persists for a perturbed