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General matrix.
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F06TFF performs the matrixcopy operation B A where A and B are m by n complex general or trapezoidal matri ..."
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Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F06TFF performs the matrixcopy operation B A where A and B are m by n complex general or trapezoidal
General matrix.
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F06QFF performs the matrixcopy operation B A where A and B are m by n real general or trapezoidal matrices ..."
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Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F06QFF performs the matrixcopy operation B A where A and B are m by n real general or trapezoidal
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
Structure of Generalized Matrix Mechanics
, 2002
"... We study a structure of a generalized matrix mechanics based on manyindex objects. It is shown that there exists a counterpart of canonical structure in classical mechanics. 1 ..."
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We study a structure of a generalized matrix mechanics based on manyindex objects. It is shown that there exists a counterpart of canonical structure in classical mechanics. 1
Generalized Matrix Algebras and Their Applications
, 2004
"... The relations between the radicals of path algebras and connectivity of directed graphs are given. The relations between radicals of generalized matrix rings and Γrings are given. All the coquasitriangular structures of group algebra kG are found when G is a finitely generated abelian group. 2000 M ..."
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The relations between the radicals of path algebras and connectivity of directed graphs are given. The relations between radicals of generalized matrix rings and Γrings are given. All the coquasitriangular structures of group algebra kG are found when G is a finitely generated abelian group. 2000
COMPUTATION OF GENERALIZED MATRIX FUNCTIONS
"... Abstract. We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. BenIsrael, Linear and Multilinear Algebra, 1(2), 1973, pp. 163–171]. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalizat ..."
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Abstract. We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. BenIsrael, Linear and Multilinear Algebra, 1(2), 1973, pp. 163–171]. Our algorithms are based on Gaussian quadrature and Golub
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
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
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Cited by 562 (20 self)
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with overwhelming probability, provided the codimension of the subspace is Ω(r(m + n) log mn), where m, n are the dimensions of the matrix, and r is its rank. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this pre
ADDITIVITY OF MAPS ON GENERALIZED MATRIX ALGEBRAS ∗
"... Abstract. In this paper, it is proven that every multiplicative bijective map, Jordan bijective map, Jordan triple bijective map on generalized matrix algebras is additive. ..."
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Cited by 6 (5 self)
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Abstract. In this paper, it is proven that every multiplicative bijective map, Jordan bijective map, Jordan triple bijective map on generalized matrix algebras is additive.
Automatically tuned linear algebra software
 CONFERENCE ON HIGH PERFORMANCE NETWORKING AND COMPUTING
, 1998
"... This paper describes an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. The production of such software for machines ranging from desktop workstations to embedded processors can be a tedious and ..."
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Cited by 478 (26 self)
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and time consuming process. The work described here can help in automating much of this process. We will concentrate our e orts on the widely used linear algebra kernels called the Basic Linear Algebra Subroutines (BLAS). In particular, the work presented here is for general matrix multiply, DGEMM. However
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