不可约非奇异M-矩阵最小特征值界的新估计

New Estimates of the Minimum Eigenvalue Bounds for Irreducible Nonsingular M-Matrices

分别给出不可约非负矩阵的上界和不可约非奇异M–矩阵逆矩阵的Hadamard积谱半径的上界,并在这两个上界中,令不可约非负矩阵的元素全为1,同时应用不可约非奇异M–矩阵的最小特征值及其逆矩阵谱半径的关系式,得到不可约非奇异M–矩阵最小特征值的新下界;理论和实例证明新界精确性有所提高。

The paper gives two upper bounds on the spectral radius of the Hadamard product for irreducible nonnegative matrix and irreducible nonsingular M–matrix, then in these upper bounds, lets the elements of irreducible nonnegative matrix be 1, uses the relationship of the minimum eigenvalue of irreducible nonsingular M–matrix and spectral radius of its inverse matrix and obtains the new lower bound of minimum eigenvalue for irreducible nonsingular M–matrix. Theory has proved that the new territories improve the corresponding results in the literature.