| Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法 |
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| 引用本文： | 谭福平,刘洪刚.Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法[J].应用数学与计算数学学报,2004,18(1):92-96. |
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| 作者姓名： | 谭福平 刘洪刚 |
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| 作者单位： | 上海大学理学院数学系,上海,200436 |
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| 摘 要： | 摘要t矩阵乘法StraSsen算法及其变形winograd算法用分而治之的方法把矩阵乘法时间复杂性由传统的D(n。)改进到0(佗kg。n.但是对于奇数阶矩阵,在划分子矩阵时,要作特殊处理才能继续使用此算法.本文提出了一种非等阶“十”字架划分方法,可以最少化填零,最大化性能,使得奇数阶矩阵乘法的时间复杂性更加接近偶数阶矩阵乘法的效果.计算实例显示该方法是有效的.
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| 关 键 词： | 矩阵乘法 Winograd算法 |
| 修稿时间： | 2004年4月1日 |
A New Scheme to Divide Odd-sized Matrices for the Winograd's Algorithm |
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| Tan Puping Liu Honggang
School of Sciences,Shanghai University,Shanghai.A New Scheme to Divide Odd-sized Matrices for the Winograd''''s Algorithm[J].Communication on Applied Mathematics and Computation,2004,18(1):92-96. |
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| Authors: | Tan Puping Liu Honggang
School of Sciences Shanghai University Shanghai |
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| Institution: | Tan Puping Liu Honggang
School of Sciences,Shanghai University,Shanghai,200436 |
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| Abstract: | Winograd's algorithm achieves its lower complexity by using a divide-and-conquer approach, but the division step must handle odd-sized matrices. We report on a dynamic cross scheme to handle odd-sized matrices, it minimizes padding and maximizes the performance of the algorithm. Performance comparisons of our scheme with that of competing schemes show that our scheme often outperforms the alternative ones. |
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| Keywords: | matrix multiplication Winograd's variant of Strassen's algorithm |
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