反循环矩阵求逆的同步算法
A Synchronous Algorithm for Anti-circular Matrix Inversion
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摘要: 反循环矩阵是一种特殊的矩阵,在其可逆的情况下,本文给出了一种求逆矩阵简单易行的办法。只需利用初等变化把Aξ0化成单位矩阵I,元素列为-ξi、-ξi+1、…、-ξn-1、ξ0、…、ξi-1的反循环矩阵Aξ1(1≤i≤n-1)的逆可同步算出,并给出了数值算法和例子验证定理的正确性。Abstract: The anti-circular matrix is a special matrix, a simple and easy method for inversion is obtained under the presense of its inverse matrix in this paper. Only Aξ0 is turned into unit matrix by using elementary transformation, the inversions of the anti-circular matrices Aξ1(1≤i≤n-1) in which their elements are listed as -ξi、-ξi+1、…、-ξn-1、ξ0、…、ξi-1can be calculated simultaneously, the numerical algorithms and examples are aslo given to verify the correctness of theories.