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Multifrontal multithreaded rankrevealing sparse QR factorization
"... SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading ..."
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Cited by 16 (2 self)
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structures are found without requiring the formation of the pattern of A T A. Rankdetection is performed within each frontal matrix using Heath’s method, which does not require column pivoting. The resulting sparse QR factorization obtains a substantial fraction of the theoretical peak performance of a
Computing RankRevealing QR Factorizations of Dense Matrices
 Argonne Preprint ANLMCSP5590196, Argonne National Laboratory
, 1996
"... this paper, and we give only a brief synopsis here. For details, the reader is referred to the code. Test matrices 1 through 5 were designed to exercise column pivoting. Matrix 6 was designed to test the behavior of the condition estimation in the presence of clusters for the smallest singular value ..."
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Cited by 39 (2 self)
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this paper, and we give only a brief synopsis here. For details, the reader is referred to the code. Test matrices 1 through 5 were designed to exercise column pivoting. Matrix 6 was designed to test the behavior of the condition estimation in the presence of clusters for the smallest singular
Codes for RankRevealing QR Factorizations of Dense Matrices
, 1996
"... This paper describes a suite of codes as well as associated testing and timing drivers for computing rankrevealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly ..."
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Cited by 1 (0 self)
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This paper describes a suite of codes as well as associated testing and timing drivers for computing rankrevealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly
An Efficient Boosting Algorithm for Combining Preferences
, 1999
"... The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new boosting ..."
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Cited by 707 (18 self)
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The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new
ON RANKREVEALING FACTORISATIONS*
"... Abstract. The problem of finding a rankrevealing QR (RRQR) factorisation of a matrix A consists of permuting the columns of A such that the resulting QR factorisation contains an upper triangular matrix whose linearly dependent columns are separated from the linearly independent ones. In this paper ..."
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Abstract. The problem of finding a rankrevealing QR (RRQR) factorisation of a matrix A consists of permuting the columns of A such that the resulting QR factorisation contains an upper triangular matrix whose linearly dependent columns are separated from the linearly independent ones
Algorithm 782: Codes for rankrevealing QR factorizations of dense matrices
 ACM Trans. Math. Software
, 1998
"... This article describes a suite of codes as well as associated testing and timing drivers for computing rankrevealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the common ..."
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Cited by 20 (0 self)
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This article describes a suite of codes as well as associated testing and timing drivers for computing rankrevealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version
Symmetric RankRevealing Decompositions
"... We develop algorithms for computing rankrevealing decompositions of symmetric matrices that exploit and inherit the symmetry, and demonstrate which particular decompositions and algorithms are useful for dense and sparse semidefinite and indefinite matrices. The most useful algorithms are based o ..."
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We develop algorithms for computing rankrevealing decompositions of symmetric matrices that exploit and inherit the symmetry, and demonstrate which particular decompositions and algorithms are useful for dense and sparse semidefinite and indefinite matrices. The most useful algorithms are based
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum
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