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On Efficient Large Sparse Matrix Chain Multiplication
Proceedings of the ACM on Management of DataSparse matrices are often used to model the interactions among different objects and they are prevalent in many areas including e-commerce, social network, and biology. As one of the fundamental matrix operations, the sparse matrix chain multiplication (SMCM) aims to efficiently multiply a chain of sparse matrices, which has found various real-world ...
Chunxu Lin +5 more
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Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product
IEEE Transactions on Computers, 1981The error complexity analysis of three algorithms for matrix multiplication and matrix chain product has been given. It is shown that the usual inner product type algorithm is by far the best algorithm for simple matrix multiplication or matrix chain product in terms of minimal basic term growth and minimal error complexities, the latter being ...
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Memory Optimized Dynamic Matrix Chain Multiplication Using Shared Memory in GPU
2020Number of multiplications needed for Matrix Chain Multiplication of \( n \) matrices depends not only on the dimensions but also on the order to multiply the chain. The problem is to find the optimal order of multiplication. Dynamic programming takes \( O\left( {n^{3} } \right) \) time, along with \( O\left( {n^{2} } \right) \) space in memory for ...
Girish Biswas, Nandini Mukherjee
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Design and implementation of GPU-based matrix chain multiplication using C++AMP
2017 Second International Conference on Electrical, Computer and Communication Technologies (ICECCT), 2017Matrix Chain Multiplication is one of the optimization problems widely used in graph algorithms, signal processing and network industry. The Matrix Chain multiplication is the process of multiplying number of nxn matrices cumulatively, where n is the size of the matrix.
K. Shyamala, K. Raj Kiran, D. Rajeshwari
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Mechanism and Machine Theory, 2020
Abstract The automatic sketching of kinematic chains (KCs) is an important part of the conceptual design of mechanisms, which is useful for the creative design of mechanisms. In this paper, a novel algorithm for automatic sketching of planar KCs with multiple joints was proposed based on joint-joint adjacent matrix (JJAM).
Wei Sun, Jianyi Kong, Liangbo Sun
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Abstract The automatic sketching of kinematic chains (KCs) is an important part of the conceptual design of mechanisms, which is useful for the creative design of mechanisms. In this paper, a novel algorithm for automatic sketching of planar KCs with multiple joints was proposed based on joint-joint adjacent matrix (JJAM).
Wei Sun, Jianyi Kong, Liangbo Sun
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Journal of Intelligent & Fuzzy Systems, 2018
Cloud computing offers an economical, convenient and elastic pool of computing resources over the internet. It enables computationally weak client to execute large computations by outsourcing their computation load to the cloud servers.
Kumar, Malay, Vardhan, Manu
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Cloud computing offers an economical, convenient and elastic pool of computing resources over the internet. It enables computationally weak client to execute large computations by outsourcing their computation load to the cloud servers.
Kumar, Malay, Vardhan, Manu
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IEEE Transactions on Computers, 2016
With growing demands in real-time control, classification or prediction, algorithms become more complex while low power and small size devices are required. Matrix multiplication (direct or transpose) is common for such computation algorithms. In numerous algorithms, it is also required to perform matrix multiplication repeatedly, where the result of a
Taras Iakymchuk +4 more
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With growing demands in real-time control, classification or prediction, algorithms become more complex while low power and small size devices are required. Matrix multiplication (direct or transpose) is common for such computation algorithms. In numerous algorithms, it is also required to perform matrix multiplication repeatedly, where the result of a
Taras Iakymchuk +4 more
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2017 International Conference on High Performance Computing & Simulation (HPCS), 2017
We are interested in an easy combinatorial optimization problem having several applications in the real world, namely the matrix chain product problem that may be solved by a well known dynamic programming algorithm (DPA). Our contribution is two-fold.
Khaoula Bezzina +2 more
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We are interested in an easy combinatorial optimization problem having several applications in the real world, namely the matrix chain product problem that may be solved by a well known dynamic programming algorithm (DPA). Our contribution is two-fold.
Khaoula Bezzina +2 more
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Sequential Optimization of Matrix Chain Multiplication Relative to Different Cost Functions
2011In this paper, we present a methodology to optimize matrix chain multiplication sequentially relative to different cost functions such as total number of scalar multiplications, communication overhead in a multiprocessor environment, etc. For n matrices our optimization procedure requires O(n3) arithmetic operations per one cost function.
Igor Chikalov +2 more
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Dynamic Programming Parallelization of Matrix Chain Multiplication on GPU: A Comparative Study
2016The dynamic programming paradigm involves various important optimization problems. The set of optimization problems includes optimal binary search tree, longest common subsequence, binary knapsack, Matrix chain multiplication (MCM), and many more. In dynamic programming problems, the MCM of n matrices comprises the computation of the parenthesization ...
Tausif Diwan, S. R. Sathe
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