分块TOEPLITZ循环阵、分块HANKEL循环阵的性质及快速算法

PROPERTIES OF TWO CLASSES BLOCK CIRCULANT MATRICES AND THEIR FAST ALGORITHMS

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))

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.