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Recent Advances in Eigenvalues Estimates of Special Matrices (Tensors)

This thematic series is devoted to publishing the latest and most significant results in eigenvalues estimates of special matrices (tensors). Its goals are to stimulate further research and to highlight recent advances in these fields as well as to promote, encourage, and bring together researchers in the fields of eigenvalues estimates of special matrices (tensors). In the last decade, spectral theory of matrices (tensors) and related topics emerged as a rapidly growing area of research because of its applications in computational mathematics, mathematical physics, mathematical economics, graph theory and wireless communications, etc. Many new results, including theory, methods and applications, have been developed during the recent years.

Edited by: Jianxing Zhao, Tomohiro Sogabe, Xianming Gu and Shiliang Wu

  1. Content type: Research

    The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, 2005) is extended t...

    Authors: Cheng-yi Zhang, Weiwei Wang, Shuanghua Luo and Jianxing Zhao

    Citation: Journal of Inequalities and Applications 2017 2017:68

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  2. Content type: Research

    Utilizing a new method to structure parallellotopes, a geometrical interpretation of the inverse matrix is given, which includes the generalized inverse of full column rank or a full row rank matrices. Further...

    Authors: Yanping Zhou and Binwu He

    Citation: Journal of Inequalities and Applications 2016 2016:257

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  3. Content type: Research

    Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in math...

    Authors: Jinxia Li, Ruirui Sun and Baode Li

    Citation: Journal of Inequalities and Applications 2016 2016:243

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  4. Content type: Research

    Some sufficient conditions are proposed in this paper such that the nonlinear eigenvalue problem with an irreducible singular M-matrix has a unique positive eigenvector. Under these conditions, the Newton-SOR ite...

    Authors: Cheng-yi Zhang, Yao-yan Song and Shuanghua Luo

    Citation: Journal of Inequalities and Applications 2016 2016:225

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  5. Content type: Research

    Some convergence conditions on successive over-relaxed (SOR) iterative method and symmetric SOR (SSOR) iterative method are proposed for non-Hermitian positive definite linear systems. Some examples are given ...

    Authors: Cheng-yi Zhang, Guangyan Miao and Yan Zhu

    Citation: Journal of Inequalities and Applications 2016 2016:156

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  6. Content type: Research

    In this paper, we present a splitting method for solving the shifted skew-Hermitian linear system, which is briefly called an α-SSS. Some convergence results are established and numerical experiments show that th...

    Authors: Angang Cui, Haiyang Li and Chengyi Zhang

    Citation: Journal of Inequalities and Applications 2016 2016:160

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  7. Content type: Research

    Several convergent sequences of the lower bounds for the minimum eigenvalue of M-matrices are given. It is proved that these sequences are monotone increasing and improve some existing results. Finally, numerical...

    Authors: Jianxing Zhao and Caili Sang

    Citation: Journal of Inequalities and Applications 2016 2016:119

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