摘要
矩阵张量积的计算是矩阵计算中的一类重要问题,与乘法相比,张量积的计算量更为庞大。分析了分块矩阵张量积的相关数学特性,证明了在置换相抵意义下两个矩阵的张量积运算可以交换,特别刻画了这类置换矩阵,并由此证明了在置换相抵条件下分块矩阵可以分块地进行张量积运算。在此基础上,讨论了矩阵张量积的并行计算问题,提出了几种并行计算模型,进行了必要的算法分析,并通过实例阐述了这些算法的思想和过程。
The matrix tensor product computation is important in matrix computation. Compared with its multiplication, the computing amount of tensor product is huger. Based on analyzing its mathematical properties. It is proved that two matrix tensor operation can be exchange at permuted similar and this kind permutation matrix is portrayed. Thus, the conclusion is obtained that tensor product of block matrixes can blocks to calculate at permuted similar. Based on these, parallel computing problem of matrix tensor product is discussed, some parallel computing models are presented, the algorithm complexity is analyzed, and the thought and process are elaborated by an example.
出处
《计算机工程与设计》
CSCD
北大核心
2007年第23期5591-5594,共4页
Computer Engineering and Design
基金
江西省自然科学基金项目(0411030)
关键词
分块矩阵
张量积
置换相抵
并行算法
计算复杂性
block matrix
tensor product
permuted similar
parallel algorithms
computational complexity
