随机搜索算法求解2×2矩阵乘法问题

Shengwen Deng, Yuren Zhou, Hua-Qing Min, Jing-Hui Zhu
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引用次数: 0

摘要

自Volker Strassen于1968年提出递归矩阵乘法算法,将时间复杂度降低到n2.81以来,许多学者在此基础上做了大量的研究。近年来,研究人员提出使用计算机算法来解决快速矩阵乘法问题。他们利用遗传算法找到了Strassen算法或其他与Strassen算法具有相同时间复杂度的算法。在本文中,我们使用随机搜索算法来寻找需要较少乘法的矩阵乘法算法。并首次采用组合高斯消去法提高了计算速度;同时对局部搜索技术进行了改进,增强了算法的局部搜索能力。在2×2矩阵的数值实验中,验证了算法的有效性。与现有的遗传算法相比,新方法具有明显的快速搜索优势,并发现了一些新的矩阵乘法算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Random search algorithm for 2×2 matrices multiplication problem
Since Volker Strassen proposed a recursive matrix multiplication algorithm reducing the time complexity to n2.81 in 1968, many scholars have done a lot of research on this basis. In recent years, researchers have proposed using computer algorithms to solve fast matrix multiplication problem. They have found Strassen's algorithm or other algorithms that have the same time complexity as Strassen algorithm by using genetic algorithm. In this paper, we used random search algorithm to find the matrix multiplication algorithms that require fewer multiplications. And we used combining Gaussian elimination for the first time to improve calculation speed; meanwhile we improved the local search technology to enhance the local search capability of the algorithm. In the numerical experiments of 2×2 matrices, the results verified the effectiveness of the algorithm. Compared with the existing genetic algorithm, the new method has obvious advantage of quick search, and found some of new matrix multiplication algorithms.
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