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The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
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Cited by 535 (17 self)
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and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificiallygenerated matrices cannot meet, and is widely used by the sparse matrix algorithms community
On matrix powers in maxalgebra
 LINEAR ALGEBRA AND ITS APPLICATIONS 421 (2007) 370–381
, 2007
"... Let A = (aij) ∈ Rn×n,N = {1,..., n} and DA be the digraph (N, {(i, j); aij> −∞}). The matrix A is called irreducible if DA is strongly connected, and strongly irreducible if every maxalgebraic power of A is irreducible. A is called robust if for every x with at least one finite component, A(k) ..."
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Cited by 6 (2 self)
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Let A = (aij) ∈ Rn×n,N = {1,..., n} and DA be the digraph (N, {(i, j); aij> −∞}). The matrix A is called irreducible if DA is strongly connected, and strongly irreducible if every maxalgebraic power of A is irreducible. A is called robust if for every x with at least one finite component, A
On Matrix Powering in Low Dimensions
"... We investigate theMatrix Powering Positivity Problem, PosMatPow: given anm×m square integer matrixM, a linear function f: Zm×m → Z with integer coefficients, and a positive integer n (encoded in binary), determine whether f(Mn) ≥ 0. We show that for fixed dimensions m of 2 and 3, this problem is de ..."
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We investigate theMatrix Powering Positivity Problem, PosMatPow: given anm×m square integer matrixM, a linear function f: Zm×m → Z with integer coefficients, and a positive integer n (encoded in binary), determine whether f(Mn) ≥ 0. We show that for fixed dimensions m of 2 and 3, this problem
Matrix Power SBox Construction ∗
"... The new symmetric cipher Sbox construction based on matrix power function is presented. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered by other matrix. The left ..."
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The new symmetric cipher Sbox construction based on matrix power function is presented. The matrix consisting of plain data bit strings is combined with three round key matrices using arithmetical addition and exponent operations. The matrix power means the matrix powered by other matrix. The left
High dimensional graphs and variable selection with the Lasso
 ANNALS OF STATISTICS
, 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
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Cited by 733 (22 self)
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The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso
Hypergraph Partitioning for Computing Matrix Powers
, 2010
"... Motivation Krylov Subspace Methods (KSMs) are a class of iterative algorithms commonly used in scientific applications for solving linear systems, eigenvalue problems, singular value problems, and least squares. Standard KSMs are communicationbound, due to a sparse matrix vector multiplication (SpM ..."
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Cited by 4 (0 self)
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MV) in each iteration. This motivated the formulation of CommunicationAvoidingKSMs, which remove the communication bottleneck to increase performance. A successful strategy for avoiding communication in KSMs uses a matrix powers kernel that exploits locality in the graph of the system matrix A. The matrix
The control of the false discovery rate in multiple testing under dependency
 Annals of Statistics
, 2001
"... Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than comparab ..."
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Cited by 1092 (16 self)
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Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR controlling procedure for independent test statistics and was shown to be much more powerful than
The Power of Convex Relaxation: NearOptimal Matrix Completion
, 2009
"... This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering. In ..."
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Cited by 356 (7 self)
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This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering
Testing for Common Trends
 Journal of the American Statistical Association
, 1988
"... Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix ..."
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Cited by 463 (7 self)
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matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic
Matrix powers in finite precision arithmetic
 SIAM J. Matrix Anal. Appl
, 1995
"... And by contacting: ..."
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