带状Toeplitz方程组的解

ON THE SOLUTION OF BANDED TOEPLITZ LINEAR SYSTEMS

本文提出求解带状 Toeplitz 线性方程组的一种新方法.其计算复杂度为O(n(p+q)),而不是一般 Toeplitz 方程组的算法的 O(n^2).这里,n 是方程的阶,p 和 q 分别是上和下半带宽.此外,该方法比用一般的带状 LU 分解方法既节省运算量,也少用计算机存贮.

A new method for solving banded Toeplitz linear systems is presented in this paper. This kind of linear systems are widely applied.The complexity of the algorithms presented here is O(n(p+q))as opposed to O(n^2),the complexity of the general algorithms for solving Toeplitz systems,where p and q are the upper and lower bandwidth respectively. Furthermore,the algorithms require less opcrations as well as storages comparing with banded LU decompositon.