Fast matrix multiplication
نویسنده
چکیده
منابع مشابه
Recursion removal in fast matrix multiplication
Recursion’s removal improves the efficiency of recursive algorithms, especially algorithms with large formal parameters, such as fast matrix multiplication algorithms. In this article, a general method of breaking recursions in fast matrix multiplication algorithms is introduced, which is generalized from recursions removal of a specific fast matrix multiplication algorithm of Winograd.
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The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...
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The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of ordern in <Cxnlos'7 operations, and, hence, the inverse of any nonsingular matrix in <Cürtlog'7 operations.
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First we study asymptotically fast algorithms for rectangular matrix multiplication. We begin with new algorithms for multiplication of an n_n matrix by an n_n matrix in arithmetic time O(n), |=3.333953..., which is less by 0.041 than the previous record 3.375477... . Then we present fast multiplication algorithms for matrix pairs of arbitrary dimensions, estimate the asymptotic running time as...
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We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63–72]. As a consequence of our analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also s...
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Abstract. On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the theoretical encoding of Strassen’s fast matrix multiplication algorithm with DNA based on an n-moduli set in the residue number system, t...
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تاریخ انتشار 2017