结式循环线性系统求解的快速算法

Fast Algorithm for Judging the Solution of Resultant Cyclic Matrix Equation

给出了一类结式循环线性系统求解的一种快速算法.当结式循环矩阵非奇异时,该快速算法可求出该线性系统的唯一解;而当结式循环矩阵奇异时,该快速算法可求出该线性系统的通解。

A fast Algorithm for judging the solution of the resultant cyclic matrix equation is presented by the fast algorithm for computing polynomials.When resultant cyclic matrices are nonsingular,the single solution of the resultant cyclic matrix equation can be found;When resultant cyclic matrices are singular,the special as well as the general solution of the resultant cyclic matrix equation can thus be found.There is only an error of approximation when the fast algorithm of computers is applied,and only the elements in the first row of the resultant cyclic matrix is used by the fast algorithm,so the result of the computation is accurate in theory.