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438
Efficient dense Gaussian elimination over the finite field with two elements. available at http://arxiv.org/abs/1111.6549
, 2011
"... In this work we describe an efficient implementation of a hierarchy of algorithms for Gaussian elimination upon dense matrices over the field with two elements (F2). We discuss both wellknown and new algorithms as well as our implementations in the M4RI library, which has been adopted into SAGE. Th ..."
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Cited by 3 (0 self)
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In this work we describe an efficient implementation of a hierarchy of algorithms for Gaussian elimination upon dense matrices over the field with two elements (F2). We discuss both wellknown and new algorithms as well as our implementations in the M4RI library, which has been adopted into SAGE
Solving Large Sparse Linear Systems Over Finite Fields
, 1991
"... Many of the fast methods for factoring integers and computing discrete logarithms require the solution of large sparse linear systems of equations over finite fields. This paper presents the results of implementations of several linear algebra algorithms. It shows that very large sparse systems can ..."
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Cited by 89 (3 self)
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be solved efficiently by using combinations of structured Gaussian elimination and the conjugate gradient, Lanczos, and Wiedemann methods. 1. Introduction Factoring integers and computing discrete logarithms often requires solving large systems of linear equations over finite fields. General surveys
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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image for each array element using discrete Fourier transform (DFT). The second step then is to create a fullFOV image from the set of intermediate images. To achieve this one must undo the signal superposition underlying the foldover effect. That is, for each pixel in the reduced FOV the signal
Dense linear algebra over finite fields: the FFLAS and FFPACK packages
, 2009
"... In the last past two decades, several efforts have been made to reduce exact linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide efficient implementations of such algorithms one need to be careful with the underlying arithmet ..."
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Cited by 7 (1 self)
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arithmetic. It is well know that modular technique such as Chinese remainder algorithm or padic lifting allow in practice to achieve better performances especially when word size arithmetic are used. Therefore, finite field arithmetics becomes an important core for efficient exact linear algebra libraries
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
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 simulation for tail probabilities of gaussian random fields
 In Proceeding of Winter Simulation Conference
, 2008
"... We are interested in computing tail probabilities for the maxima of Gaussian random fields. In this paper, we discuss two special cases: random fields defined over a finite number of distinct point and fields with finite KarhunenLoève expansions. For the first case we propose an importance sampl ..."
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Cited by 7 (5 self)
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We are interested in computing tail probabilities for the maxima of Gaussian random fields. In this paper, we discuss two special cases: random fields defined over a finite number of distinct point and fields with finite KarhunenLoève expansions. For the first case we propose an importance
EFFICIENT SIMULATION FOR TAIL PROBABILITIES OF GAUSSIAN RANDOM FIELDS
"... We are interested in computing tail probabilities for the maxima of Gaussian random fields. In this paper, we discuss two special cases: random fields defined over a finite number of distinct point and fields with finite KarhunenLoève expansions. For the first case we propose an importance sampling ..."
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We are interested in computing tail probabilities for the maxima of Gaussian random fields. In this paper, we discuss two special cases: random fields defined over a finite number of distinct point and fields with finite KarhunenLoève expansions. For the first case we propose an importance
Highly scalable parallel algorithms for sparse matrix factorization
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algo ..."
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Cited by 130 (27 self)
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present the first algorithm to factor a wide class of sparse matrices (including those arising from two and threedimensional finite element problems) that is asymptotically as scalable as dense matrix factorization algorithms on a variety of parallel architectures. Our algorithm incurs less
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method
"... New Gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method. For discontinuous functions, we construct Gausslike quadrature rules over arbitrarilyshaped elements in two dimensions without the need for partiti ..."
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Cited by 5 (1 self)
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New Gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method. For discontinuous functions, we construct Gausslike quadrature rules over arbitrarilyshaped elements in two dimensions without the need
Results 1  10
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438