由逆的三列或两列确定Toeplitz逆矩阵的一般方法

A General Method of Expressing the Inverse of a Toeplitz Matrices by Three of Two Column Vectors

在研究Toeplitz矩阵逆的第一列和逆的其他列之间的关系的基础上 ,提出了Toeplitz矩阵逆的类LU表达形式 .在证明表示形式的正确后 ,分析了计算的复杂度 .结果表明 ,采用给定的方法只要3n或 2n个元素就可以把n×n阶Toeplitz矩阵的逆表示出来 .

By researching the relation between the first column vector and another one of the inverse of a Toeplitz matrices,a LU -like expression of the inverse of a Toeplitz matrices is given in this essay.Using this method,it only need 3 n or even 2 n elements to determine the inverse of a n×n toeplitz matrices.