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Certified Sparse Linear System Solving
, 2000
"... In (Wiedemann, 1986) an algorithm is described for solving sparse linear systems over finite fields. When the system does not have the desired properties for the algorithm to work, it is preconditioned to enforce these properties. In (Kaltofen and Saunders, 1991) another way of preconditioning for t ..."
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Cited by 1 (0 self)
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In (Wiedemann, 1986) an algorithm is described for solving sparse linear systems over finite fields. When the system does not have the desired properties for the algorithm to work, it is preconditioned to enforce these properties. In (Kaltofen and Saunders, 1991) another way of preconditioning
Distributed Solution Of Sparse Linear Systems
"... We consider the solution of a linear system Ax = b on a distributed memory machine when the matrix A is large, sparse and symmetric positive de nite. In a previous paper we developed an algorithm to compute a llreducing nested dissection ordering of A on a distributed memory machine. We now develop ..."
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Cited by 12 (2 self)
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We consider the solution of a linear system Ax = b on a distributed memory machine when the matrix A is large, sparse and symmetric positive de nite. In a previous paper we developed an algorithm to compute a llreducing nested dissection ordering of A on a distributed memory machine. We now
Parallel Solution of General Sparse Linear Systems
, 1997
"... This paper discusses a few algorithms and their implementations for solving distributed general sparse linear systems. The preconditioners used are all variations of techniques originating from domain decomposition ideas. In particular we compare a number of variants of Schwarz procedures with Schur ..."
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Cited by 6 (4 self)
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This paper discusses a few algorithms and their implementations for solving distributed general sparse linear systems. The preconditioners used are all variations of techniques originating from domain decomposition ideas. In particular we compare a number of variants of Schwarz procedures
Robust Preconditioning for Sparse Linear Systems
, 1997
"... Preconditioned iterative methods have become standard linear solvers in many applications, but their limited robustness in some cases has hindered the ability to efficiently solve very large problems in some areas. This thesis proposes several new preconditioning techniques that attempt to extend th ..."
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Cited by 3 (0 self)
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Preconditioned iterative methods have become standard linear solvers in many applications, but their limited robustness in some cases has hindered the ability to efficiently solve very large problems in some areas. This thesis proposes several new preconditioning techniques that attempt to extend
Multipolebased preconditioners for large sparse linear systems
, 2003
"... Dense operators for preconditioning sparse linear systems have traditionally been considered infeasible due to their excessive computational and memory requirements. With the emergence of techniques such as block lowrank approximations and hierarchical multipole approximations, the cost of computin ..."
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Dense operators for preconditioning sparse linear systems have traditionally been considered infeasible due to their excessive computational and memory requirements. With the emergence of techniques such as block lowrank approximations and hierarchical multipole approximations, the cost
Discretisation of Sparse Linear Systems: An Optimisation Approach *
"... Abstract This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuoustime systems. We develop an optimisation procedure that yields the best approximation to the discretetime dynamical matrix with a prescribed sparsit ..."
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Abstract This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuoustime systems. We develop an optimisation procedure that yields the best approximation to the discretetime dynamical matrix with a prescribed
Parallel Frontal Solvers for Large Sparse Linear Systems
 COMPUTERS IN CHEMICAL ENGINEERING
, 2003
"... Many applications in science and engineering give rise to large sparse linear systems of equations that need to be solved as efficiently as possible. As the size of the problems of interest increases, it can become necessary to consider exploiting multiprocessors to solve these systems. We report o ..."
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Cited by 12 (2 self)
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Many applications in science and engineering give rise to large sparse linear systems of equations that need to be solved as efficiently as possible. As the size of the problems of interest increases, it can become necessary to consider exploiting multiprocessors to solve these systems. We report
On using reinforcement learning to solve sparse linear systems
 In Proceedings of the 8th International Conference on Computational Science, ICCS ’08
, 2008
"... Abstract. This paper describes how reinforcement learning can be used to select from a wide variety of preconditioned solvers for sparse linear systems. This approach provides a simple way to consider complex metrics of goodness, and makes it easy to evaluate a wide range of preconditioned solvers. ..."
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Cited by 3 (0 self)
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Abstract. This paper describes how reinforcement learning can be used to select from a wide variety of preconditioned solvers for sparse linear systems. This approach provides a simple way to consider complex metrics of goodness, and makes it easy to evaluate a wide range of preconditioned solvers
Resolution of sparse linear systems of equations: the RPK strategy
"... An over view of advanced techniques for solving large sparse linear systems of equations is presented. We are interested in the resolution of, Ax = b (1) where A is a sparse, large and nonsingular matrix. The first question is if it is better a direct or an iterative resolution. The main disadvanta ..."
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An over view of advanced techniques for solving large sparse linear systems of equations is presented. We are interested in the resolution of, Ax = b (1) where A is a sparse, large and nonsingular matrix. The first question is if it is better a direct or an iterative resolution. The main
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