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Dense Linear System of Equations
"... The linear system of equations with dense coefficient matrix is very common in science and engineering. In this paper, a parallel algorithm based on GramSchmidt QR factorization method for the exact solution of dense system of linear equations is presented. Although several parallel approaches have ..."
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The linear system of equations with dense coefficient matrix is very common in science and engineering. In this paper, a parallel algorithm based on GramSchmidt QR factorization method for the exact solution of dense system of linear equations is presented. Although several parallel approaches
Certified Dense Linear System Solving
, 2000
"... The following problems related to linear systems are studied: finding a diophantine solution; finding a rational solution; proving no diophantine solution exists; proving no rational solution exists. These problems are reduced, via randomization, to that of computing an expected constant number of r ..."
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Cited by 13 (5 self)
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of rational solutions of square nonsingular systems using adic lifting. The bit complexity of the latter problem is improved by incorporating fast arithmetic and fast matrix multiplication. The resulting randomized algorithm for certified dense linear system solving has substantially better asymptotic
Fast Solvers for Dense Linear Systems
"... It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a dense system, the time needed to solve such a system grows exponentially in the size of the sys ..."
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It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a dense system, the time needed to solve such a system grows exponentially in the size
Sparse Preconditioned Iterative Methods For Dense Linear Systems
 SIAM J. Sci. Comp
, 1992
"... Two sparse preconditioned iterative methods are presented to solve dense linear systems arising in the solution of two dimensional boundary integral equations. In the first method, the sparse preconditioner is constructed simply by choosing a small block of elements in the coefficient matrix of a de ..."
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Cited by 3 (0 self)
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Two sparse preconditioned iterative methods are presented to solve dense linear systems arising in the solution of two dimensional boundary integral equations. In the first method, the sparse preconditioner is constructed simply by choosing a small block of elements in the coefficient matrix of a
Iterative Solution of Dense Linear Systems
"... Integral equation methods have been used with great success in electromagnetic scattering calculations and in other problems involving unbounded computational domains. Their application is in many cases limited by the storage requirements of dense matrices and also by the rapidly increasing computat ..."
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Integral equation methods have been used with great success in electromagnetic scattering calculations and in other problems involving unbounded computational domains. Their application is in many cases limited by the storage requirements of dense matrices and also by the rapidly increasing
The First Annual Large Dense Linear System Survey
 Int. Rept. Univ. California, Berkeley CA
, 1991
"... In the March 24, 1991 issue of NA Digest, I submitted a questionnaire asking who was solving large dense linear systems of equations. Based on the responses, nearly all large dense linear systems today arise from either the benchmarking of supercomputers or applications involving the influence of a ..."
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Cited by 9 (2 self)
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In the March 24, 1991 issue of NA Digest, I submitted a questionnaire asking who was solving large dense linear systems of equations. Based on the responses, nearly all large dense linear systems today arise from either the benchmarking of supercomputers or applications involving the influence of a
Solving Dense Linear Systems on Graphics Processors
, 2008
"... We present several algorithms to compute the solution of a linear system of equations on a GPU, as well as general techniques to improve their performance, such as padding and hybrid GPUCPU computation. We also show how iterative refinement with mixedprecision can be used to regain full accuracy ..."
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Cited by 26 (8 self)
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We present several algorithms to compute the solution of a linear system of equations on a GPU, as well as general techniques to improve their performance, such as padding and hybrid GPUCPU computation. We also show how iterative refinement with mixedprecision can be used to regain full accuracy
Sparse Approximate Inverse Preconditioning For Dense Linear Systems Arising In Computational Electromagnetics
 Numerical Algorithms
, 1997
"... . We investigate the use of sparse approximate inverse preconditioners for the iterative solution of linear systems with dense complex coefficient matrices arising from industrial electromagnetic problems. An approximate inverse is computed via a Frobenius norm approach with a prescribed nonzero pat ..."
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Cited by 58 (21 self)
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. We investigate the use of sparse approximate inverse preconditioners for the iterative solution of linear systems with dense complex coefficient matrices arising from industrial electromagnetic problems. An approximate inverse is computed via a Frobenius norm approach with a prescribed nonzero
Lugpu: Efficient algorithms for solving dense linear systems on graphics hardware
 in SC ’05: Proceedings of the 2005 ACM/IEEE Conference on Supercomputing
, 2005
"... We present a novel algorithm to solve dense linear systems using graphics processors (GPUs). We reduce matrix decomposition and row operations to a series of rasterization problems on the GPU. These include new techniques for streaming index pairs, swapping rows and columns and parallelizing the com ..."
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Cited by 81 (2 self)
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We present a novel algorithm to solve dense linear systems using graphics processors (GPUs). We reduce matrix decomposition and row operations to a series of rasterization problems on the GPU. These include new techniques for streaming index pairs, swapping rows and columns and parallelizing
Fast and Efficient Parallel Solution of Dense Linear Systems
 Comput. Math. Appl
, 1989
"... The most efficient previously known parallel algorithms for the inversion of a nonsingular n x n matrix .4 or solving a linear system/Ix = b over the rational numbers require O(logn) time and M(n).x/ processors [provided that M(n) processors suffice in order to multiply two n x n rational matrices ..."
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Cited by 8 (3 self)
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The most efficient previously known parallel algorithms for the inversion of a nonsingular n x n matrix .4 or solving a linear system/Ix = b over the rational numbers require O(logn) time and M(n).x/ processors [provided that M(n) processors suffice in order to multiply two n x n rational
Results 1  10
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85,507