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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
Stable Distributions, Pseudorandom Generators, Embeddings and Data Stream Computation
, 2000
"... In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its coo ..."
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Cited by 324 (13 self)
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coordinates, such that given sketches C(p) and C(q) one can estimate jp \Gamma qj 1 up to a factor of (1 + ffl) with large probability. This solves the main open problem of [10]. ffl we obtain another sketch function C 0 which maps l n 1 into a normed space l m 1 (as opposed to C), such that m = m
Quantum Circuit Complexity
, 1993
"... We study a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomialsize quantum circuit. This result also enables us to construct a universal quantum compu ..."
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Cited by 320 (1 self)
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that the majority function does not have a linearsize quantum formula. Keywords. Boolean circuit complexity, communication complexity, quantum communication complexity, quantum computation AMS subject classifications. 68Q05, 68Q15 1 This research was supported in part by the National Science Foundation under
The Geography of Innovation
, 1994
"... This research examines spatial patterns of manufacturing product innovation and provides a model of factors contributing to geographic concentration of innovation. The model maintains that innovation is related to concentrations of innovative inputs, including: university R&D, industrial R&D ..."
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Cited by 310 (15 self)
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This research examines spatial patterns of manufacturing product innovation and provides a model of factors contributing to geographic concentration of innovation. The model maintains that innovation is related to concentrations of innovative inputs, including: university R&D, industrial R
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
A steepest descent method for oscillatory Riemann–Hilbert problems: asymptotics for the MKdV equation
 Ann. of Math
, 1993
"... In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory RiemannHilbert problems. Such problems arise, in particular, in evaluating the longtime behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves ..."
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Cited by 303 (27 self)
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for the MKdV equation leads to a RiemannHilbert factorization problem for a 2 × 2 matrix valued function m = m(·; x, t) analytic in C\R, (1) where m+(z) = m−(z)vx,t, z ∈ R, m(z) → I as z → ∞, m±(z) = lim ε↓0 m(z ± iε; x, t), vx,t(z) ≡ e −i(4tz3 +xz)σ3 v(z)e i(4tz 3 +xz)σ3, σ3 =
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
Errors in Cholesky and QR Downdating
, 1997
"... This paper presents a new analysis of the block downdating of a QR or Cholesky factorization in the presence of numerical errors. Let X be a block of rows of the matrix A and let A 1 be the matrix formed from the additional rows of A. Given a matrix R for which A = QR the problem is to find R such ..."
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This paper presents a new analysis of the block downdating of a QR or Cholesky factorization in the presence of numerical errors. Let X be a block of rows of the matrix A and let A 1 be the matrix formed from the additional rows of A. Given a matrix R for which A = QR the problem is to find R
QR decomposition on GPUs
 In Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units (Washington, D.C., March 08  08, 2009). GPGPU2
"... QR decomposition is a computationally intensive linear algebra operation that factors a matrix A into the product of a unitary matrix Q and upper triangular matrix R. Adaptive systems commonly employ QR decomposition to solve overdetermined least squares problems. Performance of QR decomposition i ..."
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Cited by 16 (0 self)
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QR decomposition is a computationally intensive linear algebra operation that factors a matrix A into the product of a unitary matrix Q and upper triangular matrix R. Adaptive systems commonly employ QR decomposition to solve overdetermined least squares problems. Performance of QR decomposition
Results 11  20
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