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Direct solvers for sparse matrices
 http://crd.lbl.gov/~xiaoye/SuperLU/ SparseDirectSurvey.pdf
"... Direct solvers for sparse matrices involve much more complicated algorithms than for dense matrices. The main complication is due to the need for efficient handling the fillin in the factors L and U. A typical sparse solver consists of four distinct steps as opposed to two in the dense case: 1. An ..."
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Cited by 4 (0 self)
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Direct solvers for sparse matrices involve much more complicated algorithms than for dense matrices. The main complication is due to the need for efficient handling the fillin in the factors L and U. A typical sparse solver consists of four distinct steps as opposed to two in the dense case: 1
Preconditioning By Fast Direct Solvers With Applications
, 2001
"... Fast direct solvers for vectorvalued problems with a divergence constraint; applications in fluid dynamics, linear elasticity and electromagnetics PRECONDITIONING BY FAST DIRECT SOLVERS BASIC APPROACHES ffl Domain imbedding methods aka fictitious domain methods: The problem is embedded in a larg ..."
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Fast direct solvers for vectorvalued problems with a divergence constraint; applications in fluid dynamics, linear elasticity and electromagnetics PRECONDITIONING BY FAST DIRECT SOLVERS BASIC APPROACHES ffl Domain imbedding methods aka fictitious domain methods: The problem is embedded in a
Direct Solvers for Symmetric Eigenvalue Problems
 IN MODERN METHODS AND ALGORITHMS OF QUANTUM CHEMISTRY, J. GROTENDORST (EDITOR), PROCEEDINGS, NIC SERIES VOLUME
, 2000
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Pegasos: Primal Estimated subgradient solver for SVM
"... We describe and analyze a simple and effective stochastic subgradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a singl ..."
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Cited by 542 (20 self)
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single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require Ω(1/ɛ2) iterations. As in previously devised SVM solvers, the number of iterations also scales linearly with 1/λ, where λ is the regularization parameter of SVM. For a linear kernel, the total
A fast direct solver for structured matrices
"... We have developed a fast direct solver for structured linear systems based on multilevel matrix compression. Starting with a hierarchically blockseparable matrix [2], we embed an approximation of the original matrix into a larger, but highly ..."
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We have developed a fast direct solver for structured linear systems based on multilevel matrix compression. Starting with a hierarchically blockseparable matrix [2], we embed an approximation of the original matrix into a larger, but highly
AN O(N) DIRECT SOLVER FOR INTEGRAL EQUATIONS ON THE PLANE
"... Abstract. An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that offdiagonal blocks of certain dense matrices have numerically low ..."
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Cited by 7 (0 self)
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Abstract. An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that offdiagonal blocks of certain dense matrices have numerically
Dynamic Scheduling for sparse direct Solver on NUMA architectures
 in "LNCS proceedings of PARA’2008
, 2008
"... Abstract. Over the past few years, parallel sparse direct solvers made significant progress and are now able to efficiently work on problems with several millions of equations. This paper presents some improvements on our sparse direct solver PaStiX for distributed NonUniform Memory Access architec ..."
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Cited by 2 (0 self)
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Abstract. Over the past few years, parallel sparse direct solvers made significant progress and are now able to efficiently work on problems with several millions of equations. This paper presents some improvements on our sparse direct solver PaStiX for distributed NonUniform Memory Access
Sparse Direct Solvers using ObjectOriented Methods
, 1998
"... We describe our experience in designing objectoriented software for a sparse direct solver. We discuss Spindle, a library of sparse matrix ordering codes and Oblio, a code implementing the remaining steps in a direct solver. Efficiencies comparable to procedural codes are obtained by careful im ..."
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We describe our experience in designing objectoriented software for a sparse direct solver. We discuss Spindle, a library of sparse matrix ordering codes and Oblio, a code implementing the remaining steps in a direct solver. Efficiencies comparable to procedural codes are obtained by careful
Fast Parallel Direct Solvers For Coarse Grid Problems
 J. Parallel and Distributed Computing
, 1997
"... We develop a fast direct solver for parallel solution of “coarse grid ” problems, Ax = b, such as arise when domain decomposition or multigrid methods are applied to elliptic partial differential equations in d space dimensions. The approach is based upon a (quasi) sparse factorization of the inver ..."
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Cited by 23 (4 self)
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We develop a fast direct solver for parallel solution of “coarse grid ” problems, Ax = b, such as arise when domain decomposition or multigrid methods are applied to elliptic partial differential equations in d space dimensions. The approach is based upon a (quasi) sparse factorization
Results 1  10
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87,886