| 分块TOEPLITZ循环阵、分块HANKEL循环阵的性质及快速算法 |
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| 引用本文： | 游兆永,路浩.分块TOEPLITZ循环阵、分块HANKEL循环阵的性质及快速算法[J].西安交通大学学报,1991(4). |
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| 作者姓名： | 游兆永 路浩 |
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| 作者单位： | 西安交通大学数学系
(游兆永)，西安交通大学数学系(路浩) |
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| 摘 要： | 本文讨论了分块Toeplitz循环阵,分块Hankel循环阵的性质。证明了分块Toeplitz循环阵相似于一个准对角阵;分块Hankel循环阵相似于一个结构简单的矩阵。进一步给出了这两类矩阵特征多项式的表达式。在此基础上给出两个分块Toeplitz循环阵,分块Toeplitz循环阵与分块Hankel循环阵,分块Hankel循环阵与分块Toeplitz循环阵及两个分块Hankel循环阵相乘的快速算法,两类矩阵求逆的快速算法,两类矩阵为系数的线性方程快速求解算法。算法所需运算量均为O(n~2mlgm+mn~(2.496))
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| 关 键 词： | 快速算法 Toeplitz Hankel |
PROPERTIES OF TWO CLASSES BLOCK CIRCULANT MATRICES AND THEIR FAST ALGORITHMS |
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| You Zhaoyong,Lu Hao.PROPERTIES OF TWO CLASSES BLOCK CIRCULANT MATRICES AND THEIR FAST ALGORITHMS[J].Journal of Xi'an Jiaotong University,1991(4). |
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| Authors: | You Zhaoyong Lu Hao |
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| Institution: | You Zhaoyong;Lu Hao Department of Mathematics |
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| Abstract: | It is shown that block Toeplitz circulant matrices are similar to block dia-
gonal marices and block Hankel matrices are similar to matrices with simple
construotion. Some O(n~2mlgm+mn~2.496) fast algerithms are presented for some
linear numerical algebraic problems, such as matrices multiplication, matrix in-
version and solution of system of linear equations associsted with these two cla-
sses matrices. |
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| Keywords: | fast algorithms Toeplitz Hankel |
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