论文信息 - Inequalities for the minimum eigenvalue of M-matrices

Inequalities for the minimum eigenvalue of M-matrices

Let A be a nonsingular M-matrix, and τ(A) denote its minimum eigenvalue. Shivakumar et al. [SIAM J. Matrix Anal. Appl., 17(2):298-312, 1996] presented some bounds of τ(A) when A is a weakly chained diagonally dominant M-matrix. The present paper establishes some new bounds of τ(A) for a general nonsingular M-matrix A. Numerical examples show that the results obtained are an improvement over some known results in certain cases.

Ting-Zhu Huang | Gui-Xian Tian | Tingzhu Huang | Gui-Xian Tian

[1] M. Lewin. On nonnegative matrices , 1971 .

[2] M. Fiedler,et al. An inequality for the hadamard product of an M-matrix and an inverse M-matrix , 1988 .

[3] Qiang Ye,et al. On Two-Sided Bounds Related to Weakly Diagonally Dominant M-Matrices with Application to Digital Circuit Dynamics , 1996, SIAM J. Matrix Anal. Appl..

[4] Robert J. Plemmons,et al. Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[5] Xuerong Yong,et al. On a conjecture of Fiedler and Markham , 1999 .

[6] Charles R. Johnson,et al. Topics in Matrix Analysis , 1991 .

[7] Lei Li,et al. On the Iterative Criterion for Generalized Diagonally Dominant Matrices , 2002, SIAM J. Matrix Anal. Appl..