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Parallel Algorithms for Certain Matrix Computations
"... The complexity of performing matrix computations, such as solving a linear system, inverting a nonsingular matrix or computing its rank, has received a lot of attention by both the theory and the scientific computing communities. In this paper we address some "nonclassical" matrix problems ..."
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The complexity of performing matrix computations, such as solving a linear system, inverting a nonsingular matrix or computing its rank, has received a lot of attention by both the theory and the scientific computing communities. In this paper we address some "nonclassical" matrix
Printed in Belgium On Integer Matrices Obeying Certain Matrix Equations
, 1969
"... On integer matrices obeying certain matrix equations ..."
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... 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 collaborative ..."
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Cited by 568 (23 self)
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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
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
 J. COMP. PHYS
, 1981
"... Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution ..."
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Cited by 959 (2 self)
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are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain “Property U.” Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct them, it is found helpful to introduce “parameter vectors
NonTrivial Solutions to Certain Matrix Equations
 Electronic Journal of Linear Algebra
"... Abstract. The existence of nontrivial solutions X to matrix equations of the form ..."
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Cited by 1 (1 self)
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Abstract. The existence of nontrivial solutions X to matrix equations of the form
ELA NONTRIVIAL SOLUTIONS TO CERTAIN MATRIX EQUATIONS∗
"... Abstract. The existence of nontrivial solutions X to matrix equations of the form F (X,A1,A2, · · ·,As) = G(X,A1,A2, · · ·,As) over the real numbers is investigated. Here F and G denote monomials in the (n × n)matrix X = (xij) of variables together with (n × n)matrices A1,A2, · · ·,As f ..."
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Abstract. The existence of nontrivial solutions X to matrix equations of the form F (X,A1,A2, · · ·,As) = G(X,A1,A2, · · ·,As) over the real numbers is investigated. Here F and G denote monomials in the (n × n)matrix X = (xij) of variables together with (n × n)matrices A1,A2, · · ·,As
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 886 (35 self)
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. 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
Properly discontinuous groups on certain matrix homogeneous spaces
, 1994
"... Abstract. We characterize discrete groups Γ ⊂ GL(n, R) which act properly discontinuously on the homogeneous space GL(m, R)\GL(n, R). A manifold M is called a complete locally homogeneous if M = J\H/Γ. Here H is a finite dimensional Lie group, J ⊂ H its closed Lie subgroup and Γ ⊂ H is a discrete su ..."
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Cited by 2 (1 self)
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Abstract. We characterize discrete groups Γ ⊂ GL(n, R) which act properly discontinuously on the homogeneous space GL(m, R)\GL(n, R). A manifold M is called a complete locally homogeneous if M = J\H/Γ. Here H is a finite dimensional Lie group, J ⊂ H its closed Lie subgroup and Γ ⊂ H is a discrete subgroup which acts freely and properly discontinuously on J\H. See [Gol]. In the last thirty years there was a lot of activity in the case where J is noncompact (the nonclassical
Results 1  10
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962,815