New Schemes for Solving the Principal Eigenvalue Problems of Perron-like Matrices via Polynomial Approximations of Matrix Exponentials

08/16/2020

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by   Desheng Li, et al.

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A real square matrix is Perron-like if it has a real eigenvalue s, called the principal eigenvalue of the matrix, and μ<s for any other eigenvalue μ. Nonnegative matrices and symmetric ones are typical examples of this class of matrices. The main purpose of this paper is to develop a set of new schemes to compute the principal eigenvalues of Perron-like matrices and the associated generalized eigenspaces by using polynomial approximations of matrix exponentials. Numerical examples show that these schemes are effective in practice.