A study of eigenvalue distribution of Hermitian Toeplitz matrix

• Main Authors: CHEONG SOI FONG, 張瑞鋒
• Other Authors: Tsung-Lin Lee
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/7xrky3

碩士 === 國立中山大學 === 應用數學系研究所 === 107 === Hermitian Toeplitz matrix arises from many real applications, such as solving differential equations by using finite difference method. In this paper, we consider the convergence rate of solving linear system Ax = b with the Hermitian Toeplitz matrix by using conjugate gradient method. The convergence rate of conjugate gradient method basically depends on the condition number on the matrix. We demonstrate the upper bound and lower bound of eigenvalues of Hermitian Toeplitz matrix. In the mathematical experiments, we notice that when the size of Hermitian Toeplitz matrix becomes larger, the distribution of the eigenvalues seems approach the associated distribution function.