正互反阵的一个特征值问题

AN EIGENVALUE PROBLEM OF A POSITIVE RECIPROCAL MATRIX

本文讨论层次分析方法提出的一个矩阵特征值问题:对于给定的正互反矩阵,如何修改它的一对元素使得主特征值能够减小?我们对此给出了解答。对于反复多次修改,我们构造了一个迭代程序并且证明了一定意义下的收敛性。将本文的结果应用于层次分析法,可以减少决策分析过程的盲目性。

Let matric A=[aij] be positive reciprocal, i.e.au=1/aji for all i,j. The problem of how to revise a pair of elements (aij, aji) such that it will lead a descent in the principal eigenvalue is studied. A solution for his problem is given. For the repeated revision, an iterative procedure is constructed and its convergence is also proved.