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Adaptive sparse matrix-matrix multiplication on the GPU
Proceedings of the 24th Symposium on Principles and Practice of Parallel Programming, 2019In the ongoing efforts targeting the vectorization of linear algebra primitives, sparse matrix-matrix multiplication (SpGEMM) has received considerably less attention than sparse Matrix-Vector multiplication (SpMV). While both are equally important, this disparity can be attributed mainly to the additional formidable challenges raised by SpGEMM.
Martin Winter +4 more
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Proceedings of the third annual ACM symposium on Theory of computing - STOC '71, 1971
This paper deals with three aspects of algebraic complexity. The first section is concerned with lower bounds on the number of operations required to compute several functions. Several theorems are presented and their proofs sketched. The second section deals with relationships among the complexities of several sets of functions.
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This paper deals with three aspects of algebraic complexity. The first section is concerned with lower bounds on the number of operations required to compute several functions. Several theorems are presented and their proofs sketched. The second section deals with relationships among the complexities of several sets of functions.
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Optimizing Sparse Matrix—Matrix Multiplication for the GPU
ACM Transactions on Mathematical Software, 2015Sparse matrix--matrix multiplication (SpGEMM) is a key operation in numerous areas from information to the physical sciences. Implementing SpGEMM efficiently on throughput-oriented processors, such as the graphics processing unit (GPU), requires the programmer to expose substantial fine-grained parallelism while conserving the limited off-chip memory ...
Dalton, Steven +2 more
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Hypercube matrix multiplication
Parallel Computing, 1993A matrix multiplication algorithm for parallel computers (hypercubes) is given. The algorithm has running times of \(O(n)\) and \(O(\log n)\) for \(n^ 2\) and \(n^ 3/2\) processors. The sub matrices are sent in a single communication to directly connected processors in the hypercube and are also involved in sequential matrix multiplication at each ...
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2020 Eighth International Symposium on Computing and Networking Workshops (CANDARW), 2020
Basic Linear Algebra Subprograms (BLAS) is a frequently used numerical library for linear algebra computations. However, it places little emphasis on computational accuracy, especially with respect to the accuracy assurance of the results. Consequently, a high-precision matrix–matrix multiplications algorithm that assures the precision by double ...
Fumiya Ishiguro +3 more
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Basic Linear Algebra Subprograms (BLAS) is a frequently used numerical library for linear algebra computations. However, it places little emphasis on computational accuracy, especially with respect to the accuracy assurance of the results. Consequently, a high-precision matrix–matrix multiplications algorithm that assures the precision by double ...
Fumiya Ishiguro +3 more
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Matrix multiplication with DNA
Journal of Molecular Evolution, 1997A DNA-based method for calculating the product of Boolean matrices or matrices containing positive, real numbers is presented. In the case of matrices containing real numbers, the manipulation of reaction conditions allows a quantitative calculation to be performed. The use of DNA to perform an analog calculation illustrates a new approach to computing
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On the asymptotic complexity of matrix multiplication
22nd Annual Symposium on Foundations of Computer Science (sfcs 1981), 1981The main results of this paper have the following flavor: Given one algorithm for multiplying matrices, there exists another, better, algorithm.
Don Coppersmith, Shmuel Winograd
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A Robust Matrix-Multiplication Array
IEEE Transactions on Computers, 1984Summary: Matrix multiplication algorithms have been proposed for VLSI array processors. Random defects in the silicon wafer and fabrication errors render processors and data paths in the array faulty, and may cause the algorithm to fail despite a significant number of nonfaulty processors.
Peter J. Varman +2 more
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A note on boolean matrix multiplication
Information Processing Letters, 1984'Almost all' known Boolean matrix multiplication algorithms are considered as an extension of algorithms for general matrix multiplication. \textit{N. Santoro} [Numer. Math. Comput., Proc. 10th Manitoba Conf., 1980, Congr. Numerantium 31, 241-251 (1981; Zbl 0507.68023)] presented \(O(n^ 2)\) algorithms under the assumption that one of the matrices is ...
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On the Additive Complexity of Matrix Multiplication
SIAM Journal on Computing, 1976A graph-theoretic model is introduced for bilinear algorithms. This facilitates in particular the investigation of the additive complexity of matrix multiplication. The number of additions/subtractions required for each of the problems defined by symmetric permutations on the dimensions of the matrices are shown to differ conversely as the size of each
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