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82,577
Implicit schemes and LU decompositions
 Mathematics of Computation
, 1981
"... Implicit methods for hyperbolic equations are analyzed using LU decompositions. It is shown that the inversion of the resulting tridiagonal matrices is usually stable even when diagonal dominance is lost. Furthermore, these decompositions can be used to construct stable algorithms in multidimensions ..."
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Cited by 12 (3 self)
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Implicit methods for hyperbolic equations are analyzed using LU decompositions. It is shown that the inversion of the resulting tridiagonal matrices is usually stable even when diagonal dominance is lost. Furthermore, these decompositions can be used to construct stable algorithms
Randomized LU Decomposition
, 2013
"... We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be parallelized and further accelerated by using sparse random ma ..."
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We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be parallelized and further accelerated by using sparse random
STATIC LU DECOMPOSITION ON HETEROGENEOUS PLATFORMS
 INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS 2001; 15; 310
, 2001
"... In this paper, the authors deal with algorithmic issues on heterogeneous platforms. They concentrate on dense linear algebra kernels, such as matrix multiplication or LU decomposition. Blockcyclic distribution techniques used in ScaLAPACK are no longer sufficient to balance the load among processor ..."
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Cited by 7 (0 self)
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In this paper, the authors deal with algorithmic issues on heterogeneous platforms. They concentrate on dense linear algebra kernels, such as matrix multiplication or LU decomposition. Blockcyclic distribution techniques used in ScaLAPACK are no longer sufficient to balance the load among
Gaussian Elimination and LUDecomposition
, 2014
"... Solving a set of linear equations arises in many contexts in applied mathematics. At least until recently, a claim could be made that solving sets of linear equations (generally as a component of dealing with larger problems like partialdifferentialequation solving, or optimization, consumes more ..."
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Solving a set of linear equations arises in many contexts in applied mathematics. At least until recently, a claim could be made that solving sets of linear equations (generally as a component of dealing with larger problems like partialdifferentialequation solving, or optimization, consumes more computer time than any other computational procedure. (Distant competitors would be the GramSchmidt process and the fast Fourier transform computation, and the GramSchmidt process is a first cousin to the Gaussian elimination computation since both may be used to solve systems of linear equations, and they are both based on forming particular linear combinations of a given sequence of vectors.) Indeed, the invention of the electronic digital computer was largely motivated by the desire to find a laborsaving means to solve systems of linear equations [Smi10]. Often the subject of linear algebra is approached by starting with the topic of solving sets of linear equations, and Gaussian elimination methodology is elaborated to introduce matrix inverses, rank, nullspaces, etc. We have seen above that computing a preimage vector x ∈ Rn of a vector v ∈ Rk with respect to the n × k matrix A consists of finding a solution (x1,..., xn) to the k linear equations: A11x1 +A21x2 + · · ·+An1xn = v1 A12x1 +A22x2 + · · ·+An2xn = v2
Locality Of Reference In Lu Decomposition With Partial Pivoting
 SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
, 1997
"... This paper presents a new partitioned algorithm for LU decomposition with partial pivoting. The new algorithm, called the recursively partitioned algorithm, is based on a recursive partitioning of the matrix. The paper analyzes the locality of reference in the new algorithm and the locality of refer ..."
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Cited by 94 (8 self)
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This paper presents a new partitioned algorithm for LU decomposition with partial pivoting. The new algorithm, called the recursively partitioned algorithm, is based on a recursive partitioning of the matrix. The paper analyzes the locality of reference in the new algorithm and the locality
LUDecomposition on a Massively Parallel Transputer System
 PROCEEDINGS OF THE 5TH INTERNATIONAL PARLE CONFERENCE ON PARALLEL ARCHITECTURES AND LANGUAGES EUROPE  LECTURE NOTES OF COMPUTER SCIENCE VOL 694
, 1993
"... Two algorithms for LUdecomposition on a transputer based reconfigurable MIMD parallel computer with distributed memory have been analyzed in view of the interdependence of granularity and execution time. In order to investigate this experimentally, LUdecomposition algorithms have been implemented ..."
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Two algorithms for LUdecomposition on a transputer based reconfigurable MIMD parallel computer with distributed memory have been analyzed in view of the interdependence of granularity and execution time. In order to investigate this experimentally, LUdecomposition algorithms have been implemented
Classification Using Efficient LU Decomposition in Sensornets
 Proceedings of WSN 2006
, 2006
"... We consider the popular application of detection, classification and tracking and their feasibility in resource constrained sensornets. We concentrate on the classification aspect, by decomposing the complex, computationally intensive signal processing MaximumAPosterior (MAP) classifier into simpl ..."
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Cited by 1 (1 self)
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into simpler computationally and communicationally load balanced procedures, using a clustering approach. LU decomposition is an efficient approach for computing the inverse of covariance matrices required in the MAP classifier. We thus explore feasibility of LU decomposition in sensornets. We present power
Resultant Matrices in ALP: LU Decomposition for Sparse Matrices
, 2001
"... There are several linear algebra packages available from many research institutions. However, there is no generic LU decomposition package specialized for sparse matrices available. This paper details the work done during the summer of 2001 towards integrating such a package to ALP, a package under ..."
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There are several linear algebra packages available from many research institutions. However, there is no generic LU decomposition package specialized for sparse matrices available. This paper details the work done during the summer of 2001 towards integrating such a package to ALP, a package under
The Hierarchical Basis Multigrid Method And Incomplete LU Decomposition
 In Seventh International Symposium on Domain Decomposition Methods for Partial Differential Equations
, 1994
"... . A new multigrid or incomplete LU technique is developed in this paper for solving large sparse algebraic systems from discretizing partial differential equations. By exploring some deep connection between the hierarchical basis method and incomplete LU decomposition, the resulting algorithm can be ..."
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Cited by 27 (7 self)
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. A new multigrid or incomplete LU technique is developed in this paper for solving large sparse algebraic systems from discretizing partial differential equations. By exploring some deep connection between the hierarchical basis method and incomplete LU decomposition, the resulting algorithm can
Results 1  10
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82,577