Toeplitz矩阵循环延拓后的特征值数值分析

Eigenvalue analysis of circulant matrices extended from the Toeplitz matrices

本文采用数值分析的方法探讨Toeplitz矩阵延拓成ω循环矩阵时特征值的逼近程度.对于对称共轭型Toeplitz矩阵,采用ω=±i时对应的循环矩阵特征值的逼近程度较好;对于其它Toeplitz矩阵,采用共轭转置将其转化为对称共轭型矩阵后,才有利于特征值的逼近.可将本文方法广泛应用于地球物理中的数值计算(如位场计算、信号处理中的反褶积、地震资料的偏移处理等).

This paper discusses how co circulant matrices approach Toeplitz matrices and the changes in the corresponding eigenvalues. For symmetric conjugate Toeplitz matrices, choosing ω=±i circulant matrices can approach perfectly~ while for any other Toeplitz mactrices, applying conjugate operators to them to become symmetric conjugate ones and then, a good approach of eigenvalues can often be expected. The ideas in the paper can be widely used geophysical computation such as potential field, deconvolution and migration of seismic data.