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On Coneigenvalues of a Complex Square Matrix
"... Abstract. In this paper, we show that a matrix A 2 Mn(C) that has n coneigenvectors, where coneigenvalues associated with them are distinct, is condiagonalizable. And also show that if all coneigenvalues of conjugatenormal matrix A be real, then it is symmetric. ..."
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Abstract. In this paper, we show that a matrix A 2 Mn(C) that has n coneigenvectors, where coneigenvalues associated with them are distinct, is condiagonalizable. And also show that if all coneigenvalues of conjugatenormal matrix A be real, then it is symmetric.
Algorithms for Nonnegative Matrix Factorization
 In NIPS
, 2001
"... Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
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Cited by 1246 (5 self)
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Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 653 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
A HeteroskedasticityConsistent Covariance Matrix Estimator And A Direct Test For Heteroskedasticity
, 1980
"... This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator ..."
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Cited by 3211 (5 self)
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This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator
A generalized leastsquare matrix decomposition
 Journal of the American Statistical Association
"... Variables in many massive highdimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatialtemporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often result ..."
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Cited by 13 (6 self)
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to a transposable quadratic norm, our decomposition, entitled the Generalized least squares Matrix Decomposition (GMD), directly accounts for structural relationships. As many variables in highdimensional settings are often irrelevant or noisy, we also regularize our matrix decomposition by adding
ChiSquare matrix: an approach for buildingblock identification
 M.J. Maher (Ed.): 9th Asian Computing Science Conference, 2004
"... Abstract. This paper presents a line of research in genetic algorithms (GAs), called buildingblock identification. The building blocks (BBs) are common structures inferred from a set of solutions. In simple GA, crossover operator plays an important role in mixing BBs. However, the crossover probabl ..."
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Cited by 7 (6 self)
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) and hierarchically decomposable functions (HDFs). In terms of scalability, our approach shows a polynomial relationship between the number of function evaluations required to reach the optimum and the problem size. A comparison between the chisquare matrix and the hierarchical Bayesian optimization algorithm (h
2009) Subspace duality in the inversion of square matrix polynomials
"... Abstract. We present duality results for subspaces involved in the inversion of square matrix polynomials with real coefficients. These results characterize left and right null spaces of the inverse in terms of subspaces associated with the original matrix polynomial. 1. Notation We present dualit ..."
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Cited by 2 (2 self)
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Abstract. We present duality results for subspaces involved in the inversion of square matrix polynomials with real coefficients. These results characterize left and right null spaces of the inverse in terms of subspaces associated with the original matrix polynomial. 1. Notation We present
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 907 (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
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 989 (4 self)
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Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares
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