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Optimizing Hardware Accelerated General Matrix-Matrix Multiplication for CNNs on FPGAs
IEEE Transactions on Circuits and Systems - II - Express Briefs, 2020Convolution is inarguably the most complex operation utilized in Convolutional Neural Networks (convnets). Owing to the billions of independent multiply-adds involved, convolution is being massively parallelized by the simultaneous utilization of many ...
Afzal Ahmad, M. A. Pasha
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IEEE Transactions on Parallel and Distributed Systems, 2019
General sparse matrix-sparse matrix multiplication (SpGEMM) is one of the fundamental linear operations in a wide variety of scientific applications.
Yuedan Chen +5 more
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General sparse matrix-sparse matrix multiplication (SpGEMM) is one of the fundamental linear operations in a wide variety of scientific applications.
Yuedan Chen +5 more
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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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Avoiding matrix multiplication
1991The 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
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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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Journal of Computational Chemistry, 1987
AbstractSeveral implementations of matrix multiplication (MMUL) in Fortran and VAX assembly language are discussed. On a VAX‐11/780 computer, the most efficient MMUL is achieved through vector‐scalar‐multiply‐and‐add (VSMA) operations, rather than by means of dot products.
Carlos F. Bunge, Gerardo Cisneros
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AbstractSeveral implementations of matrix multiplication (MMUL) in Fortran and VAX assembly language are discussed. On a VAX‐11/780 computer, the most efficient MMUL is achieved through vector‐scalar‐multiply‐and‐add (VSMA) operations, rather than by means of dot products.
Carlos F. Bunge, Gerardo Cisneros
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Three-Dimensional nand Flash for Vector–Matrix Multiplication
IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2019Three-Dimensional NAND flash technology is one of the most competitive integrated solutions for the high-volume massive data storage. So far, there are few investigations on how to use 3-D NAND flash for in-memory computing in the neural network ...
Panni Wang +6 more
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1990
Suppose that two n×n matrices A [0:n-1, 0:n-1] and B[0:n-1, 0:n-1] are to be multiplied on an SIMD hypercube to get the product matrix C where $$ C[i,j] = \sum\limits_{k = 0}^{n - 1} {A[i,k]*B[k,j],0 \le i,j < n} $$
Sanjay Ranka, Sartaj Sahni
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Suppose that two n×n matrices A [0:n-1, 0:n-1] and B[0:n-1, 0:n-1] are to be multiplied on an SIMD hypercube to get the product matrix C where $$ C[i,j] = \sum\limits_{k = 0}^{n - 1} {A[i,k]*B[k,j],0 \le i,j < n} $$
Sanjay Ranka, Sartaj Sahni
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SPARSE MATRIX–VECTOR MULTIPLICATION
2004Abstract This chapter introduces irregular algorithms and presents the example of parallel sparse matrix-vector multiplication (SpMV), which is the central operation in iterative linear system solvers. The irregular sparsity pattern of the matrix does not change during the multiplication, which may be repeated many times.
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Parallel matrix multiplication
2018 41st International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), 2018Utilizing 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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