【摘要】 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).更多还原

【Abstract】 This paper discusses how ω 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.更多还原