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Integrated photonic 3D tensor processing engine. [PDF]

Light Sci Appl
Wu Y, Ni Z, Li X, Wang Y, Lu L, Chen J, Zhou L.   +6 more
europepmc   +1 more source

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On the Number of Multiplications Required for Matrix Multiplication

SIAM Journal on Computing, 1976
In this paper we give a new algorithm for matrix multiplication which for n large uses $n^2 + o(n^2 )$ multiplications to multiply $n \times p$ matrices by $p \times n$ matrices provided $p \leqq \log _2 n$. Multiplication and division by 2 is necessary in this algorithm.
David Dobkin, Roger W Brockett
exaly   +3 more sources

Matrix algorithms on a hypercube I: Matrix multiplication

Parallel Computing, 1987
Thorough analysis of the matrix multiplication on a hypercube. Decomposition into square blocks and mapping onto a 2-D mesh of processors is optimal.
G C Fox
exaly   +2 more sources

Partial and Total Matrix Multiplication

SIAM Journal on Computing, 1981
In 1979 considerable progress was made in estimating the complexity of matrix multiplication. Here the new techniques and recent results are presented, based upon the notion of approximate rank and the observation that certain patterns of partial matrix multiplication (some of the entries of the matrices may be zero) can efficiently be utilized to ...
exaly   +3 more sources

Threaded Accurate Matrix-Matrix Multiplications with Sparse Matrix-Vector Multiplications

2018 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), 2018
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. Although some algorithms for ensuring the computational accuracy of BLAS operations have been studied, there is a ...
Shuntaro Ichimura, Takahiro Katagiri, Katsuhisa Ozaki, Takeshi Ogita, Toru Nagai   +4 more
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Matrix multiplication on LUCAS

1983 IEEE 6th Symposium on Computer Arithmetic (ARITH), 1983
Multiplication of two N by N matrices involves N3 multiplications of elements. The task allows a large amount of parallelism to be utilized, indicating that it can be efficiently executed on a parallel computer. This paper describes how matrix multiplication is performed on LUCAS, an SIMD type parallel processor with bit-serial processing elements. The
Lennart Ohlsson, Bertil Svensson
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Parallel matrix multiplication

2018 41st International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), 2018
Utilizing all CPU cores available for numerical computations is a topic of considerable interest in HPC. This paper analyzes and compares four different parallel algorithms for matrix multiplication without block partitioning using OpenMP. The comparison of the algorithms is based on the achieved speed, memory bandwidth and efficient use of the cache ...
Nikola Tomikj, Marjan Gusev
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Matrix sparsification for coded matrix multiplication

2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2017
Coded computation is a framework for providing redundancy in distributed computing systems to make them robust to slower nodes, or stragglers. In a recent work of Lee et al., the authors propose a coded computation scheme for distributedly computing A x x in the presence of stragglers. The proposed algorithm first encodes the data matrix A to obtain an
Geewon Suh, Kangwook Lee 0001, Changho Suh   +2 more
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Avoiding matrix multiplication

1991
The fastest known algorithms for many problems on graphs use matrix multiplication as a sub-routine. Some examples of problems solved using matrix multiplication are recognition of transitive graphs, computing the transitive closure of a directed acyclic graph, and finding the neighborhood containment matrix of a graph.
Tze-Heng Ma, Jeremy P. Spinrad
openaire   +1 more source