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QR Factorization Householder Transformations
"... For given m × n matrix A, with m> n, QR factorization has form A = Q R O where matrix Q is m×m and orthogonal, and R is n × n and upper triangular Can be used to solve linear systems, least squares problems, etc. As with Gaussian elimination, zeros are introduced successively into matrix A, event ..."
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For given m × n matrix A, with m> n, QR factorization has form A = Q R O where matrix Q is m×m and orthogonal, and R is n × n and upper triangular Can be used to solve linear systems, least squares problems, etc. As with Gaussian elimination, zeros are introduced successively into matrix A
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
MULTIPLICATIVE PERTURBATION ANALYSIS FOR QR FACTORIZATIONS
"... (Communicated by Wenyu Sun) Abstract. This paper is concerned with how the QR factors change when a real matrix A suffers from a left or right multiplicative perturbation, where A is assumed to have full column rank. It is proved that for a left multiplicative perturbation the relative changes in th ..."
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Cited by 1 (0 self)
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(Communicated by Wenyu Sun) Abstract. This paper is concerned with how the QR factors change when a real matrix A suffers from a left or right multiplicative perturbation, where A is assumed to have full column rank. It is proved that for a left multiplicative perturbation the relative changes
QR factorization for the Cell Broadband Engine
, 2009
"... The QR factorization is one of the most important operations in dense linear algebra, offering a numerically stable method for solving linear systems of equations including overdetermined and underdetermined systems. Modern implementations of the QR factorization, such as the one in the LAPACK libra ..."
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Cited by 10 (7 self)
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The QR factorization is one of the most important operations in dense linear algebra, offering a numerically stable method for solving linear systems of equations including overdetermined and underdetermined systems. Modern implementations of the QR factorization, such as the one in the LAPACK
and skinny qr factorizations in mapreduce architectures
 in Proceedings of the second international workshop on MapReduce and its applications
, 2011
"... The QR factorization is one of the most important and useful matrix factorizations in scientific computing. A recent communicationavoiding version of the QR factorization trades flops for messages and is ideal for MapReduce, where computationally intensive processes operate locally on subsets of ..."
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Cited by 8 (3 self)
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The QR factorization is one of the most important and useful matrix factorizations in scientific computing. A recent communicationavoiding version of the QR factorization trades flops for messages and is ideal for MapReduce, where computationally intensive processes operate locally on subsets
Componentwise Perturbation Analyses for the QR Factorization
"... This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, Q T Q = I, R upper triangular, for a given real m n matrix A of rank n. Such specic analyses are important for example when the columns of A are badly scaled. First order perturbation bounds are given ..."
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Cited by 8 (4 self)
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This paper gives componentwise perturbation analyses for Q and R in the QR factorization A = QR, Q T Q = I, R upper triangular, for a given real m n matrix A of rank n. Such specic analyses are important for example when the columns of A are badly scaled. First order perturbation bounds
On the Perturbation of LU, Cholesky, and QR Factorizations
 SIAM Journal on Matrix Analysis and Applications
"... In this paper error bounds are derived for a first order expansion of the LU factorization of a perturbation of the identity. The results are applied to obtain perturbation expansions of the LU, Cholesky, and QR factorizations. This report is available by anonymous ftp from thales.cs.umd.edu in th ..."
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In this paper error bounds are derived for a first order expansion of the LU factorization of a perturbation of the identity. The results are applied to obtain perturbation expansions of the LU, Cholesky, and QR factorizations. This report is available by anonymous ftp from thales
On the Perturbation of LU, Cholesky, and QR Factorizations
 SIAM Journal on Matrix Analysis and Applications
"... In this paper error bounds are derived for a first order expansion of the LU factorization of a perturbation of the identity. The results are applied to obtain perturbation expansions of the LU, Cholesky, and QR factorizations. This report is available by anonymous ftp from thales.cs.umd.edu in th ..."
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In this paper error bounds are derived for a first order expansion of the LU factorization of a perturbation of the identity. The results are applied to obtain perturbation expansions of the LU, Cholesky, and QR factorizations. This report is available by anonymous ftp from thales
Results 1  10
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103,016