| 一种求布尔矩阵传递闭包的基于自反矩阵构造的平方算法 |
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| 引用本文： | 谷云东,赵峰.一种求布尔矩阵传递闭包的基于自反矩阵构造的平方算法[J].数学的实践与认识,2007,37(1):55-60. |
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| 作者姓名： | 谷云东 赵峰 |
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| 作者单位： | 1. 华北电力大学(北京)数理学院,北京,102206;北京师范大学管理学院,北京,100875
2. 聊城大学数学科学学院,山东,聊城,252059 |
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| 基金项目： | 国家自然科学基金;国家重点基础研究发展计划(973计划);中国博士后科学基金 |
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| 摘 要： | 首先,介绍布尔矩阵传递闭包的概念及计算问题;随后,分析布尔矩阵的传递闭包和由该布尔矩阵与单位矩阵取并所得到的自反矩阵的传递闭包之间的关系;最后,利用上述结果给出一种求解布尔矩阵传递闭包的基于自反矩阵构造的平方算法,并通过实例说明了其具体计算过程.
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| 关 键 词： | 布尔矩阵 传递闭包 自反矩阵 平方算法 |
| 修稿时间： | 2005年9月16日 |
A Reflexive Matrix Constructing based Square Algorithm for Calculating the Transitive Closure of Boolean Matrix |
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| GU Yun-dong,ZHAO Feng.A Reflexive Matrix Constructing based Square Algorithm for Calculating the Transitive Closure of Boolean Matrix[J].Mathematics in Practice and Theory,2007,37(1):55-60. |
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| Authors: | GU Yun-dong ZHAO Feng |
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| Abstract: | First,the transitive closure of general boolean matrix and it′s computing problems are discussed.Then,the relations between the transitive closure of general boolean matrix and that of the reflexive boolean matrix constructed by the union of boolean matrix and identity matrix are studied.At last,the reflexive matrix contracting based square algorithm is presented for calculating the transitive closure of the general binary relation,and the procedure of it is showed through an example. |
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| Keywords: | boolean matrix transitive closure reflexive matrix square algorithm |
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