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1
Content available remote

New bounds for the minimum eigenvalue ofM-matrices

100%
Wang F., Sun D.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1007-1013
EN
Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
2
Content available remote

A convergence analysis of SOR iterative methods for linear systems with weakH-matrices

76%
Zhang C.-y., Xue Z., Luo S.
Open Mathematics
|
2016
|
tom 14
|
nr 1
747-760
EN
It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.
3
Content available remote

Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

76%
Zhao J., Sang C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
81-88
EN
Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.
4
Content available remote

AnS-type upper bound for the largest singular value of nonnegative rectangular tensors

76%
Zhao J., Sang C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
925-933
EN
An S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (2011). Numerical examples are given to verify the theoretical results.
5
Content available remote

New bounds for the minimum eigenvalue of 𝓜-tensors

76%
Zhao J., Sang C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
296-303
EN
A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.
6
Content available remote

Two new eigenvalue localization sets for tensors and theirs applications

76%
Zhao J., Sang C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1267-1276
EN
A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50). As an application, a weaker checkable sufficient condition for the positive (semi-)definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1), 187-198). As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.
7
Content available remote

Approximation of eigenvalues for unbounded Jacobi matrices using finite submatrices

64%
Monvel A., Zielinski L.
Open Mathematics
|
2014
|
tom 12
|
nr 3
445-463
EN
We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.
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