A method for computing the Perron-Frobenius root for primitive matrices

07/09/2019

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by   Doulaye Dembélé, et al.

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For a nonnegative matrix, the eigenvalue with the maximum magnitude or Perron-Frobenius root exists and is unique if the matrix is primitive. It is shown that for a primitive matrix A, there exists a positive rank one matrix X allowing to have the Hadamard product B = A ∘ X, where the row (column) sums of matrix B are the same and equal to the Perron-Frobenius 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.