摘要
利用两个线性方程组是否有解给出了Toeplitz矩阵可逆的条件,表明Toeplitz矩阵之逆阵可以表示为φ-循环矩阵与上三角Toeplitz矩阵的乘积之和,给出了其逆矩阵列的递推公式,得到了求Toeplitz矩阵之逆矩阵的快速算法.讨论了此新分解式的稳定性,证明了此分解式是向前稳定的,并确定了其运算量.
In this paper, we conclude that a Toeplitz matrix is invertible if two systems of Toeplitz equations are slovable. The inverse matrix can be denoted as a sum of products of φ-circulant matrices and upper triangular Toeplitz matrices. The stability and operation of the inversion formula for Toeplitz matrices are also considered.
出处
《淮海工学院学报(自然科学版)》
CAS
2007年第3期13-15,共3页
Journal of Huaihai Institute of Technology:Natural Sciences Edition