| 引用本文: | 曾泳泓.某些环中卷积的快速计算.[J].国防科技大学学报,1990,12(3):63-69.[点击复制] |
| Zeng Yonghong.Fast Computation for Convolutions in Some Rings[J].Journal of National University of Defense Technology,1990,12(3):63-69[点击复制] |
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| 某些环中卷积的快速计算 |
| 曾泳泓 |
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(系统工程与应用数学系)
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| 摘要: |
| 本文研究了环中卷积的快速计算问题，讨论了计算域中卷积通常使用的Winograd 短卷积算法、快速富里叶变换算法以及多项式变换算法对一般环中卷积计算的可适用性。特别地，对应用广泛的矩阵多项式乘积、矩阵卷积及多项式卷积计算提出了比直接计算快得多的算法。 |
| 关键词: 近世代数，环，卷积，快速算法 |
| DOI： |
| 投稿日期：1987-03-12 |
| 基金项目: |
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| Fast Computation for Convolutions in Some Rings |
| Zeng Yonghong |
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(Department of Applied Mathematics and System Engineering)
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| Abstract: |
| This paper discusses the problem of fast computation of convolutions in rings. The adaptability of the well-known Winograd algorithm，FPT algorithm and FFT algorithm which are proposed for computing convolutions in complex fields is studied in the case of rings. Especially，fast algorithms for computing multiplication of matrix polynomial，matrix convolution and polynomial convolution are proposed. They are of wide practical usage. |
| Keywords: modern algebra,ring,convolution,fast algorithm |
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