The Calculation Of Heimitian Toeplitz Matrix-vector Product

This thesis concerns the computation of hermitian Toeplitz matrix-vector product. Exploiting the structure and properties of hermitian Toeplitz matrices, we first transform an hermitian Toeplitz matrix into the sum of a real Toeplitz matrix and a Hankel matrix. Then we develop three fast algorithms for computing the hermitian Toeplitz matrix-vector product, which are based on embedded method, multilevel method and splitting method via FFT approach, respectively. Finally, we give a numerical experiment to show the computational costs of the above three algorithms and a comparison of our algorithms with the conventional algorithm.This thesis consists of five chapters which are organized as follows:The first chapter is an introduction. We mainly introduce the background, the main contents and the originalities of the thesis.In the second chapter, we briefly review some basic definition and notation which will be used in sequel.In the third chapter, we develop a fast algorithm for computing the hermitian Toeplitz matrix-vector product in which a Toeplitz matrix is first embedded in a circulant matrix and then an FFT procedure follows.In the fourth chapter, we develop a fast algorithm for computing the hermitian Toeplitz matrix-vector product in which a multi-level idea is applied.In the fifth chapter, we develop a fast algorithm for computing the hermitian Toeplitz matrix-vector product in which a real symmetric Toeplitz matrix is split into a sum of a circulant and skew-circulant matrix and then a FFT procedure follows.