A diagonal transformation-based algorithm for computing the minimum eigenvalue of irreducible <i>M</i>-matrices

This study presents a novel algorithm for computing the minimum eigenvalue of irreducible M-matrices. Firstly, we introduce a new diagonal transformation technique and establish sharper two-sided bounds for the spectral radius of irreducible nonnegative matrices with positive diagonal entries. Building upon these theoretical foundations, we develop an efficient iterative algorithm to compute the minimum eigenvalue of irreducible M-matrices. The convergence of the proposed algorithm is rigorously proved, ensuring both computational stability and asymptotic accuracy. Numerical experiments demonstrate the effectiveness of the method, showing that it achieves high precision with relatively low computational cost compared to existing approaches.