2020
DOI: 10.48550/arxiv.2008.06850
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New Schemes for Solving the Principal Eigenvalue Problems of Perron-like Matrices via Polynomial Approximations of Matrix Exponentials

Abstract: A real square matrix is Perron-like if it has a real eigenvalue s, called the principal eigenvalue of the matrix, and Re 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 … Show more

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“…Various numerical schemes such as the Euler scheme, walk on sphere schemes and walk on rectangles schemes are considered in [1]. In [4], Li and Wang considered a family of Perron-like matrices and investigated the principal eigenvalues and the associated generalized eigen-spaces via polynomial approximations of matrix exponentials. For some closely-related developments on the computation of eigen-pairs for matrices, we refer to [5,6,7,8,9,10,12,13,14,15] and the references therein for more extensive discussions.…”
Section: Introductionmentioning
confidence: 99%
“…Various numerical schemes such as the Euler scheme, walk on sphere schemes and walk on rectangles schemes are considered in [1]. In [4], Li and Wang considered a family of Perron-like matrices and investigated the principal eigenvalues and the associated generalized eigen-spaces via polynomial approximations of matrix exponentials. For some closely-related developments on the computation of eigen-pairs for matrices, we refer to [5,6,7,8,9,10,12,13,14,15] and the references therein for more extensive discussions.…”
Section: Introductionmentioning
confidence: 99%