A new algorithm to compute the inverse of a nonsingular r circulant matrix over any one number field is presented by Euclidean algorithm. The algorithm does not need to compute the triangular function and has little count of work.

• 利用欧几里德算法给出了任意数域上非奇异 r -循环矩阵求逆矩阵的一个新算法 ,该方法不需要计算三角函数并且具有很少的计算量