期刊论文

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

中文

数学理论与应用

1006-8074

2017

37

3

38-42

国家自然科学基金资助项目(11371075).

本校为第一机构

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/√2 (I-iJ),we develop a more efficient algorithm that only O(n) complex arithmetics are included...