论文标题
通过矩阵指数的多项式近似，用于解决Perron样矩阵的主要特征值问题的新方案
New Schemes for Solving the Principal Eigenvalue Problems of Perron-like Matrices via Polynomial Approximations of Matrix Exponentials
论文作者
论文摘要
如果真正的特征值$ s $，则称为矩阵的主要特征值，而$ \ mbox {re} \，μ<s $，用于任何其他eigenvalue $μ$，则像perron一样。非负矩阵和对称的矩阵是此类矩阵的典型示例。本文的主要目的是开发一组新方案，以通过使用矩阵指数的多项式近似值来计算perron样矩阵的主要特征值和相关的广义特征空间。数值示例表明，这些方案在实践中是有效的。
A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,μ<s$ 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 are effective in practice.
