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EXPLOITING MULTIPLE LEVELS OF PARALLELISM IN SPARSE MATRIXMATRIX MULTIPLICATION
"... Abstract. Sparse matrixmatrix multiplication (or SpGEMM) is a key primitive for many highperformance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2. ..."
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Abstract. Sparse matrixmatrix multiplication (or SpGEMM) is a key primitive for many highperformance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2
Highly Parallel Sparse MatrixMatrix Multiplication
, 2010
"... Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on ..."
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Cited by 16 (4 self)
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Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based
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 GPU General Sparse MatrixMatrix Multiplication for Irregular Data
"... Abstract—General sparse matrixmatrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle ext ..."
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Abstract—General sparse matrixmatrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
Challenges and advances in parallel sparse matrixmatrix multiplication
 In The 37th International Conference on Parallel Processing (ICPP’08
, 2008
"... We identify the challenges that are special to parallel sparse matrixmatrix multiplication (PSpGEMM). We show that sparse algorithms are not as scalable as their dense counterparts, because in general, there are not enough nontrivial arithmetic operations to hide the communication costs as well as ..."
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Cited by 24 (6 self)
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We identify the challenges that are special to parallel sparse matrixmatrix multiplication (PSpGEMM). We show that sparse algorithms are not as scalable as their dense counterparts, because in general, there are not enough nontrivial arithmetic operations to hide the communication costs as well
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 766 (23 self)
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illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem
Sparse Bayesian Learning and the Relevance Vector Machine
, 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vec ..."
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Cited by 958 (5 self)
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This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classication tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 930 (41 self)
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In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many
Results 1  10
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