Some New Bounds on the Minimum Eigenvalue of Nonsingular M -Matrices

نویسندگان

  • Zhengge Huang
  • Zhong Xu
چکیده

If A is a nonsingular M -matrix, some new upper and lower bounds on the minimum eigenvalue τ(A) of A are given. These bounds improve some results of Tian and Huang and are more accurate than Li et al. in some cases. In addition, we obtain some new bounds on the minimum eigenvalue of a nonsingular M -matrix A , which can give affirmative conclusions about whether bounds for the minimum eigenvalue of a general nonsingular M -matrix A are only depending on the entries of A and they are easy to calculate. Mathematics Subject Classification: 15A06, 15A42, 15A48

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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 ...

متن کامل

Ela 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 ...

متن کامل

The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices

The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced....

متن کامل

Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(A B) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M -matrices A and B are given. Some results of comparison are also given in theory. To illustrate ou...

متن کامل

Ela a New Eigenvalue Bound for the Hadamard Product of an M-matrix and an Inverse M-matrix

If A and B are n× n nonsingular M -matrices, a new lower bound for the minimum eigenvalue τ(A◦B) for the Hadamard product of A and B is derived. This bound improves the result of [R. Huang. Some inequalities for the Hadamard product and the Fan product of matrices. Linear Algebra Appl., 428:1551–1559, 2008.].

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015