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Strategies for Preconditioning Methods of Parallel Iterative Solvers . . .
, 2009
"... Solving largescale systems of linear equations [] { } {}bxA = is one of the most expensive and critical processes in scientific computing. In particular, for simulation codes based on the finiteelement method (FEM), most of the computational time is devoted to solving linear equation systems wit ..."
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with sparse coefficient matrices. For this reason, a significant proportion of scalable algorithm research and development is aimed at solving these large, sparse linear systems of equations on parallel computers. Sparse linear solvers can be broadly classified as being either direct or iterative. Direct
LSRN: A parallel iterative solver for strongly over or underdetermined systems
, 2011
"... Abstract. We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the minlength solution to minx∈Rn ‖Ax − b‖2, where A ∈ Rm×n with m n or m n, and where A may be rankdeficient. Tikhonov regularization may also be included. Since A ..."
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Cited by 16 (6 self)
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Abstract. We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the minlength solution to minx∈Rn ‖Ax − b‖2, where A ∈ Rm×n with m n or m n, and where A may be rankdeficient. Tikhonov regularization may also be included. Since
Parallel Iterative Solvers with Selective Blocking Preconditioning for Simulations of Fault Zone Contact
 2001 International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Industrial Applications (Preconditioning 2001), Tahoe City
, 2001
"... Iterative solver with preconditioning is the most powerful choice for largescale scientific computation, especially for the parallel computing. In nonlinear problems such as contact simulations for geophysics, the condition numbers of the coefficient matrices are usually large due to special constr ..."
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Cited by 3 (3 self)
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Iterative solver with preconditioning is the most powerful choice for largescale scientific computation, especially for the parallel computing. In nonlinear problems such as contact simulations for geophysics, the condition numbers of the coefficient matrices are usually large due to special
Convergence Acceleration Method of LargeScale Parallel Iterative Solvers for Heterogeneous Properties
"... In largescale scientific computing, linear sparse solver is one of the most timeconsuming process. In GeoFEM, various types of preconditioned iterative method is implemented on massively parallel computers. It has been wellknown that ILU(0) factorization is very effective preconditioning metho ..."
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In largescale scientific computing, linear sparse solver is one of the most timeconsuming process. In GeoFEM, various types of preconditioned iterative method is implemented on massively parallel computers. It has been wellknown that ILU(0) factorization is very effective preconditioning
Parallel Iterative Solvers and Preconditioners Using Approximate Hierarchical Methods (Extended Abstract)
, 1996
"... ) Ananth Grama, Vipin Kumar, Ahmed Sameh Department of Computer Science, University of Minnesota Minneapolis, MN 55455 {ananth, kumar, sameh}@cs.umn.edu Abstract In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods ..."
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) Ananth Grama, Vipin Kumar, Ahmed Sameh Department of Computer Science, University of Minnesota Minneapolis, MN 55455 {ananth, kumar, sameh}@cs.umn.edu Abstract In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element
Parallel Iterative Solvers for Irregular Sparse Matrices in High Performance Fortran
, 1997
"... Writing efficient iterative solvers for irregular sparse matrices in HPF is hard. The locality in the computations is unclear, and for efficiency we use storage schemes that obscure any structure in the matrix. Moreover, the limited capabilities of HPF to distribute and align data structures make it ..."
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Cited by 1 (0 self)
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Writing efficient iterative solvers for irregular sparse matrices in HPF is hard. The locality in the computations is unclear, and for efficiency we use storage schemes that obscure any structure in the matrix. Moreover, the limited capabilities of HPF to distribute and align data structures make
Parallel Iterative Solvers for Unstructured Grids using an OpenMP/MPI Hybrid Programming Model for the GeoFEM
 Platform on SMP Cluster Architectures, submitted to WOMPEI 2002 (International Workshop on OpenMP: Experiences and Implementations), Kansai Science City
, 2002
"... Abstract. An efficient parallel iterative method for unstructured grids developed by the authors for SMP cluster architectures on the GeoFEM platform is presented. The method is based on a 3level hybrid parallel programming model, including message passing for interSMP node communication, loop dir ..."
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Cited by 16 (10 self)
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Abstract. An efficient parallel iterative method for unstructured grids developed by the authors for SMP cluster architectures on the GeoFEM platform is presented. The method is based on a 3level hybrid parallel programming model, including message passing for interSMP node communication, loop
Parallel iterative solvers of geofem with selective blocking preconditioning for nonlinear contact problems on the earth simulator
 In: SC ’03: Proceedings of the 2003 ACM/IEEE conference on Supercomputing
, 2003
"... An efficient parallel iterative method with selective blocking preconditioning has been developed for symmetric multiprocessor (SMP) cluster architectures with vector processors such as the Earth Simulator. This method is based on a threelevel hybrid parallel programming model, which includes messa ..."
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Cited by 8 (2 self)
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An efficient parallel iterative method with selective blocking preconditioning has been developed for symmetric multiprocessor (SMP) cluster architectures with vector processors such as the Earth Simulator. This method is based on a threelevel hybrid parallel programming model, which includes
1 Parallel Iterative Solvers with the Selective Blocking Preconditioning for Simulations of FaultZone Contact
"... Iterative solver with preconditioning is the most powerful choice for largescale scientific computation, especially for the parallel computing. In nonlinear problems such as contact simulations for geophysics, the condition numbers of the coefficient matrices are usually large due to special const ..."
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Iterative solver with preconditioning is the most powerful choice for largescale scientific computation, especially for the parallel computing. In nonlinear problems such as contact simulations for geophysics, the condition numbers of the coefficient matrices are usually large due to special
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
Results 1  10
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