基于一类本原矩阵的非负矩阵Perron根的算法

An algorithm for calculating Perron roots of nonnegative matrix based on a kind of primitive matrix

利用矩阵的对角相似变换和Perron-Frobenius定理,给出了一类迹非零的不可约非负矩阵Perron根的简单数值算法,该算法仅需在迭代的每一步选择上次迭代矩阵的行和构成的正对角矩阵做矩阵的相似变换.同时通过适当的矩阵平移,此算法可适用于所有不可约非负矩阵Perron根的计算.

Using the diagonal similarity transformation and Perron-Frobenius theorem of matrix, a simple numerical algorithm for calculating Perron roots of a class of irreducible nonnegative matrix with nonzero trace is given. In this algorithm, it only needs to choose the positive diagonal matrix composed of the row sums of last iterative matrix in every step of the iteration and to do similarity transformation of matrix. At the same time, through proper matrix translation, this algorithm is applicable to the calculation of Perron roots of all irreducible nonnegative matrices.