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496
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
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Cited by 773 (23 self)
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, the nonsymmetric eigenvalue problem, and the singular value decomposition. We consider dense, band and sparse matrices.
Efficient Multiplication of Dense Matrices over GF(2)
, 2008
"... We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (F2). In particular we present our implementation – in the M4RI library – of StrassenWinograd matrix multiplication and the “Method of the Four Russians” multip ..."
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Cited by 5 (0 self)
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We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (F2). In particular we present our implementation – in the M4RI library – of StrassenWinograd matrix multiplication and the “Method of the Four Russians
Algorithm XXX: Efficient Multiplication of Dense Matrices over GF(2)
"... We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (F2). In particular we present our implementation – in the M4RI library – of StrassenWinograd matrix multiplication and the “Method of the Four Russians for Mul ..."
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We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (F2). In particular we present our implementation – in the M4RI library – of StrassenWinograd matrix multiplication and the “Method of the Four Russians
Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine
 SIMvl Review
, 1984
"... Abstract. This paper examines common implementations of linear algebra algorithms, such as matrixvector multiplication, matrixmatrix multiplication and the solution of linear equations. The different versions are examined for efficiency on a computer architecture which uses vector processing and ha ..."
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Cited by 70 (14 self)
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Abstract. This paper examines common implementations of linear algebra algorithms, such as matrixvector multiplication, matrixmatrix multiplication and the solution of linear equations. The different versions are examined for efficiency on a computer architecture which uses vector processing
Efficient Decomposition of Dense Matrices over GF(2
 in "Proceedings of the Workshop on Tools for Cryptanalysis", jun 2010, arXiv:1006.1744 [cs.MS
"... Abstract. In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (F2). Matrix decomposition is an essential building block for solving dense systems of linear and nonlinear equations and thus much re ..."
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Cited by 3 (0 self)
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Abstract. In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (F2). Matrix decomposition is an essential building block for solving dense systems of linear and nonlinear equations and thus much
Efficient sparse matrixvector multiplication on CUDA
, 2008
"... The massive parallelism of graphics processing units (GPUs) offers tremendous performance in many highperformance computing applications. While dense linear algebra readily maps to such platforms, harnessing this potential for sparse matrix computations presents additional challenges. Given its rol ..."
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Cited by 113 (2 self)
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role in iterative methods for solving sparse linear systems and eigenvalue problems, sparse matrixvector multiplication (SpMV) is of singular importance in sparse linear algebra. In this paper we discuss data structures and algorithms for SpMV that are efficiently implemented on the CUDA platform
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect
Implementing sparse matrixvector multiplication on throughputoriented processors
 In SC ’09: Proceedings of the 2009 ACM/IEEE conference on Supercomputing
, 2009
"... Sparse matrixvector multiplication (SpMV) is of singular importance in sparse linear algebra. In contrast to the uniform regularity of dense linear algebra, sparse operations encounter a broad spectrum of matrices ranging from the regular to the highly irregular. Harnessing the tremendous potential ..."
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Cited by 142 (7 self)
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Sparse matrixvector multiplication (SpMV) is of singular importance in sparse linear algebra. In contrast to the uniform regularity of dense linear algebra, sparse operations encounter a broad spectrum of matrices ranging from the regular to the highly irregular. Harnessing the tremendous
Understanding the Efficiency of GPU Algorithms for MatrixMatrix Multiplication
, 2004
"... Utilizing graphics hardware for general purpose numerical computations has become a topic of considerable interest. The implementation of streaming algorithms, typified by highly parallel computations with little reuse of input data, has been widely explored on GPUs. We relax the streaming model&a ..."
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Cited by 95 (1 self)
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's constraint on input reuse and perform an indepth analysis of dense matrixmatrix multiplication, which reuses each element of input matrices O(n) times. Its regular data access pattern and highly parallel computational requirements suggest matrixmatrix multiplication as an obvious candidate
AN EFFICIENT AND STABLE METHOD FOR PARALLEL FACTORIZATION OF DENSE SYMMETRIC INDEFINITE MATRICES
"... This paper investigates the efficient parallelization of algorithms with strong stability guarantees to factor dense symmetric indefinite matrices. It shows how the bounded BunchKaufman algorithm may be efficiently parallelized, and then how its performance can be enhanced by using exhaustive block ..."
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Cited by 2 (0 self)
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This paper investigates the efficient parallelization of algorithms with strong stability guarantees to factor dense symmetric indefinite matrices. It shows how the bounded BunchKaufman algorithm may be efficiently parallelized, and then how its performance can be enhanced by using exhaustive
Results 1  10
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496