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Linear Algebra Operators for GPU Implementation of Numerical Algorithms
 ACM Transactions on Graphics
, 2003
"... In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for ..."
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Cited by 317 (9 self)
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direct solvers for sparse matrices, and by applying these solvers to multidimensional finite difference equations, i.e. the 2D wave equation and the incompressible NavierStokes equations.
PSPASES: An Efficient and Scalable Parallel Sparse Direct Solver
 IN PROCEEDINGS OF THE NINTH SIAM CONFERENCE ON PARALLEL PROCESSING FOR SCIENTIFIC COMPUTING
, 1999
"... Many problems in engineering and scientific domains require solving large sparse systems of linear equations, as a computationally intensivesteptowards the final solution. It has long beenachallenge to develop efficient parallel formulations of sparse direct solvers due to several different complex ..."
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Cited by 5 (2 self)
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Many problems in engineering and scientific domains require solving large sparse systems of linear equations, as a computationally intensivesteptowards the final solution. It has long beenachallenge to develop efficient parallel formulations of sparse direct solvers due to several different complex
Objectoriented design for sparse direct solvers
 Institute for Computer
, 1999
"... Abstract. We discuss the objectoriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important ..."
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Cited by 4 (0 self)
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Abstract. We discuss the objectoriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe
The Design of I/OEfficient Sparse Direct Solvers
"... We consider two problems related to I/O: First, find the minimum primary memory size required to factor a sparse, symmetric matrix when permitted to read and write the data exactly once. Second, find the minimum data traffic between core and external memory when permitted to read and write the data ..."
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Cited by 1 (0 self)
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We consider two problems related to I/O: First, find the minimum primary memory size required to factor a sparse, symmetric matrix when permitted to read and write the data exactly once. Second, find the minimum data traffic between core and external memory when permitted to read and write the data
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
Iterative And Direct Sparse Solvers On Parallel Computers
, 1996
"... This paper addresses the main issues raised during the parallelization of iterative and direct solvers for such systems in distributed memory multiprocessors. If no preconditioning is considered, iterative solvers are simple to parallelize, as the most timeconsuming computational structures are mat ..."
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are matrix vector products. Direct methods are much harder to parallelize, as new nonzero values may appear during computation and pivoting operations are usually accomplished due to numerical stability considerations. Suitable data structures and distributions for sparse solvers are discussed within
Sparse Iterative Solvers for Circuit Simulation
"... One important mathematical problem in simulation of large electrical circuits is the solution of highdimensional linear equation systems. The corresponding matrices are real, nonsymmetric, very illconditioned, have an irregular sparsity pattern, and include a few dense rows and columns. ..."
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One important mathematical problem in simulation of large electrical circuits is the solution of highdimensional linear equation systems. The corresponding matrices are real, nonsymmetric, very illconditioned, have an irregular sparsity pattern, and include a few dense rows and columns.
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
SparseMatrixCGSolver in CUDA
"... This paper describes the implementation of a parallelized conjugate gradient solver for linear equation systems using CUDAC. Given a real, symmetric and positive definite coefficient matrix and a righthand side, the parallized cgsolver is able to find a solution for that system by exploiting the ..."
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This paper describes the implementation of a parallelized conjugate gradient solver for linear equation systems using CUDAC. Given a real, symmetric and positive definite coefficient matrix and a righthand side, the parallized cgsolver is able to find a solution for that system by exploiting
Results 11  20
of
135,747