Results 221 to 230 of about 303,055 (260)
Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion [PDF]
SIAM Journal of Scientific Computing, 2015 In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity.
Ming-Jun Lai +2 more
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Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xinlong Feng
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xinlong Feng
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Decreasing the Displacement Rank of a Matrix
SIAM Journal on Matrix Analysis and Applications, 1993Für eine \(n\times n\)-Matrix \(S\) sei \(W(S)=S-ZSZ^ T\), wobei \(Z\) nur in der ersten Subdiagonalen Einsen und sonst Nullen aufweist. Zwei \(n\times d\)-Matrizen \(G,H\) werden ein \(d\)-Generator (displacement) von \(S\) der Länge \(d\) genannt, wenn \(W(S)=GH^ T\) erfüllt ist.
VÍCTOR Pan
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On the Matrix-Cut Rank of Polyhedra
Mathematics of Operations Research, 2001Lovász and Schrijver (1991) described a semidefinite operator for generating strong valid inequalities for the 0-1 vectors in a prescribed polyhedron. Among their results, they showed that n iterations of the operator are sufficient to generate the convex hull of 0-1 vectors contained in a polyhedron in n-space.
William J. Cook, Sanjeeb Dash
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Mathematics Magazine, 1968
Let A = (aij) be an n X m matrix with entries in a field F. Each of the n rows -of A can be regarded as a vector in coordinate m-space, Fm, and each of the m columns of A can be regarded as a vector in Fn. The row space of A is the subspace of Fin spanned by the rows of A and column space of A is the subspace of F71 spanned by the columns of A. The row
V. C. Williams, F. S. Cater
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Let A = (aij) be an n X m matrix with entries in a field F. Each of the n rows -of A can be regarded as a vector in coordinate m-space, Fm, and each of the m columns of A can be regarded as a vector in Fn. The row space of A is the subspace of Fin spanned by the rows of A and column space of A is the subspace of F71 spanned by the columns of A. The row
V. C. Williams, F. S. Cater
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Canadian Journal of Mathematics, 1958
This paper continues a study appearing in (5) of the combinatorial properties of a matrix A of m rows and n columns, all of whose entries are 0's and 1's. Let the sum of row i of A be denoted by ri and let the sum of column i of A be noted by st. We call R = (r1, … , rm) the row sum vector and S = (s1, … , sn) the column sum vector of A.
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This paper continues a study appearing in (5) of the combinatorial properties of a matrix A of m rows and n columns, all of whose entries are 0's and 1's. Let the sum of row i of A be denoted by ri and let the sum of column i of A be noted by st. We call R = (r1, … , rm) the row sum vector and S = (s1, … , sn) the column sum vector of A.
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A New Approximation of the Matrix Rank Function and Its Application to Matrix Rank Minimization
Journal of Optimization Theory and Applications, 2013The author considers the NP-hard matrix rank minimization problem which has a variety of applications, eg in control, signal processing and system identification. New approximation functions are introduced which have general properties of generic approximation functions, eg controllability of accuracy.
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Matrix semigroups with commutable rank
Semigroup Forum, 2003The authors study complex matrix semigroups (and algebras) on which rank is commutable (i.e., \(\text{rank}(AB)=\text{rank}(BA)\)). It is shown that in a number of cases (e.g., in dimension \(\leq 6\)), but not always, commutativity of rank entails permutability of rank (i.e., \(\text{rank}(A_1A_2\cdots A_n)=\text{rank}(A_{\sigma(1)}A_{\sigma(2)}\cdots
Livshits, L. +4 more
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Proceedings of the 2009 international symposium on Symbolic and algebraic computation, 2009
For the problem of computing the rank of a matrix we have a complexity result and a practical implementation, both of which apply best to the case of a matrix whose rank is substantially smaller than its order.First, matrix rank can be computed in essentially optimal time when the rank is sufficiently small, specifically when the rank is less than the ...
B. David Saunders, Bryan S. Youse
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For the problem of computing the rank of a matrix we have a complexity result and a practical implementation, both of which apply best to the case of a matrix whose rank is substantially smaller than its order.First, matrix rank can be computed in essentially optimal time when the rank is sufficiently small, specifically when the rank is less than the ...
B. David Saunders, Bryan S. Youse
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The Term and Stochastic Ranks of a Matrix
Canadian Journal of Mathematics, 1959The term rank p of a matrix is the order of the largest minor which has a non-zero term in the expansion of its determinant. In a recent paper (1), the authors made the following conjecture. If S is the sum of all the entries in a square matrix of non-negative real numbers and if M is the maximum row or column sum, then the term rank p of the matrix is
Dulmage, A. L., Mendelsohn, N. S.
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