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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
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
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
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 2 (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
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
Parallel Direct Methods For Sparse Linear Systems
, 1997
"... We present an overview of parallel direct methods for solving sparse systems of linear equations, focusing on symmetric positive definite systems. We examine the performance implications of the important differences between dense and sparse systems. Our main emphasis is on parallel implementation of ..."
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Cited by 7 (0 self)
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We present an overview of parallel direct methods for solving sparse systems of linear equations, focusing on symmetric positive definite systems. We examine the performance implications of the important differences between dense and sparse systems. Our main emphasis is on parallel implementation
A Parallel Balanced Method for Sparse Linear Systems
, 1997
"... A scalable parallel algorithm is proposed for the solution of general, nonsingular sparse linear systems. The linear system is partitioned into blocks of rows with a small number of unknowns common to multiple blocks. Our technique yields a reduced system defined only on these common unknowns which ..."
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A scalable parallel algorithm is proposed for the solution of general, nonsingular sparse linear systems. The linear system is partitioned into blocks of rows with a small number of unknowns common to multiple blocks. Our technique yields a reduced system defined only on these common unknowns which
A restricted additive Schwarz preconditioner for general sparse linear systems
 SIAM J. Sci. Comput
, 1999
"... Abstract. We introduce some cheaper and faster variants of the classical additive Schwarz preconditioner (AS) for general sparse linear systems and show, by numerical examples, that the new methods are superior to AS in terms of both iteration counts and CPU time, as well as the communication cost w ..."
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Cited by 127 (22 self)
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Abstract. We introduce some cheaper and faster variants of the classical additive Schwarz preconditioner (AS) for general sparse linear systems and show, by numerical examples, that the new methods are superior to AS in terms of both iteration counts and CPU time, as well as the communication cost
Results 1  10
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2,546,286