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.
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)
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).
