Following the Perron theorem, the spectral radius of a primitive matrix is a simple eigenvalue. It is shown that for a primitive matrix A, there is a positive rank one matrix X such that B = A ∘ X, where ∘ denotes the Hadamard product of matrices, and such that the row (column) sums of matrix B are the same and equal to the Perron root. An iterative algorithm is presented to obtain matrix B without an explicit knowledge of X. The convergence rate of this algorithm is similar to that of the power method but it uses less computational load. A byproduct of the proposed algorithm is a new method for calculating the first eigenvector.

中文翻译：

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一种计算原始矩阵的Perron根的方法

根据Perron定理，基本矩阵的谱半径是一个简单的特征值。结果表明，对于一个原始矩阵甲，有一个正的秩一点矩阵X，使得乙 = 甲 ∘  X，其中∘表示矩阵的Hadamard乘积，并且使得矩阵的行（列）总和乙是相同的等于Perron根 提出了一种迭代算法来获得矩阵B，而无需明确了解X。该算法的收敛速度类似于幂方法的收敛速度，但是它使用较少的计算量。该算法的副产品是计算第一特征向量的新方法。