Hermitian Toeplitz矩阵向量乘积的快速算法  

A Fast Algorithm for Computing Products of Hermitian Toeplitz Matrices and Vectors

作　　者：刘仲云 陈思恒 徐伟进 张育林 Liu Zhongyun;Chen Siheng;Xu Weijin;Zhang Yulin(School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China;Centro de Matemdtica,Universidade do Minho,4710--057Braga,Portugal)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410114 [2]Minho大学数学中心,葡萄牙4710—057

出　　处：《数学理论与应用》2017年第3期38-42,共5页Mathematical Theory and Applications

基　　金：国家自然科学基金资助项目(11371075).

摘　　要：众所周知,大规模Hermitian Toeplitz矩阵向量乘积Ax可由快速Fourier变换(FFT)进行计算.事实上,Hermitian Toeplitz矩阵在酉相似变换下可约化为一个实的Toeplitz矩阵与Hankel矩阵之和.基于此,本文利用DCT和DST,构造了一个更有效的方法,只需O(n)的复运算.It is known that the product Ax of a large scale Hermitian Toeplitz matrix A and a vector x can be computed effectively by using the Fast Fourier Transform (FFT).In this paper,based on the fact that an Hermitian Toeplitz matrix A can be reduced into a real Toeplitz--plus--Hankel matrix (A =T+H )by a unitary similarity transformation (the unitary matrix is U=1/√2I-iJ),we develop a more efficient algorithm that only O(n)complex arithmetics are included for computing the product Ax by employing the DCT and DST.

关 键 词：HERMITIAN TOEPLITZ矩阵 矩阵向量乘法 DCT DST 实运算 

分 类 号：O151.21[理学—数学]