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Extended Irreducible Nekrasov Matrices as Subclasses of Irreducible H-Matrices

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Abstract

In this paper, we introduce the irreducible \(\alpha \)-Nekrasov matrices and irreducible \(\alpha \)-S-Nekrasov matrices as the extended irreducible Nekrasov matrices and we analyze the relationships among the involved matrices and irreducible H-matrices.

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References

  1. Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. Classics in Applied Mathematics. SIAM, Philadelphia (1994)

    Book  Google Scholar 

  2. Huang, T.-Z., Ran, R.-S.: A simple estimation for the spectral radius of (block) \(H\)-matrices. J. Comput. Appl. Math. 177, 455–459 (2005). https://doi.org/10.1016/j.cam.2004.09.059

    Article  MathSciNet  MATH  Google Scholar 

  3. Liu, J.-Z., Huang, Y.-Q.: Some properties on Schur complements of \(H\)-matrices and diagonally dominant matrices. Linear Algebra Appl. 389, 365–380 (2004). https://doi.org/10.1016/j.laa.2004.04.012

    Article  MathSciNet  MATH  Google Scholar 

  4. Li, W.: On Nekrasov matrices. Linear Algebra Appl. 281, 87–96 (1998). https://doi.org/10.1016/S0024-3795(98)10031-9

    Article  MathSciNet  MATH  Google Scholar 

  5. Cvetković, L., Dai, P.-F., K. Doroslovac̆ki, and Y.-T. Li, : Infinity norm bounds for the inverse of Nekrasov matrices. Appl. Math. Comput. 219, 5020–5024 (2013). https://doi.org/10.1016/j.amc.2012.11.056

  6. Pang, M.-X., Li, Z.-X.: Generalized Nekrasov matrices and applications. J. Comput. Math. 21, 183–188 (2003)

    MathSciNet  MATH  Google Scholar 

  7. Cvetković, L., Kostić, V., S. Raus̆ki, : A new subclass of \(H\)-matrices. Appl. Math. Comput. 208, 206–210 (2009). https://doi.org/10.1016/j.amc.2008.11.037

  8. Sun, Y.-X.: Sufficient conditions for generalized diagonally dominant matrices. Numer. Math. J. Chinese Univ. 3, 216–223 (1997). (Chinese)

    MATH  Google Scholar 

  9. Gan, T.-B., Huang, T.-Z.: Simple criteria for nonsingular \(H\)-matrices. Linear Algebra Appl. 374, 317–326 (2003). https://doi.org/10.1016/S0024-3795(03)00646-3

    Article  MathSciNet  MATH  Google Scholar 

  10. Huang, T.-Z.: A note on generalized diagonally dominant matrices. Linear Algebra Appl. 225, 237–242 (1995). https://doi.org/10.1016/0024-3795(93)00368-A

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, J.-Z., He, A.-Q.: Simple criteria for generalized diagonally dominant matrices. Int. J. Comput. Math. 85, 1065–1072 (2008). https://doi.org/10.1080/00207160701472469

    Article  MathSciNet  MATH  Google Scholar 

  12. Cvetković, L., Kostić, V.: New criteria for identifying \(H\)-matrices. J. Comput. Appl. Math. 180, 265–278 (2005). https://doi.org/10.1016/j.cam.2004.10.017

    Article  MathSciNet  MATH  Google Scholar 

  13. Bru, R., Corral, C., Giménez, I., Mas, J.: Classes of general \(H\)-matrices. Linear Algebra Appl. 429, 2358–2366 (2008). https://doi.org/10.1016/j.laa.2007.10.030

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, J.-Z., Zhang, J., Zhou, L.-X., et al.: The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications[J]. Appl. Math. Comput. 320, 251–263 (2018)

    MathSciNet  MATH  Google Scholar 

  15. Li, C.-Q., Pei, H., Gao, A.-N., et al.: Improvements on the infinity norm bound for the inverse of Nekrasov matrices[J]. Numerical Algorithms 71(3), 613–630 (2016)

    Article  MathSciNet  Google Scholar 

  16. L.-Yu Kolotilina, : Some characterizations of Nekrasov andS-Nekrasov matrices[J]. J. Math. Sci. 207(5), 767–775 (2015)

  17. Liu, J.-Z., Wang, L.-L., Lyu, Z.-H.: Several criteria for judging H- and non-H-matrices[J]. Int. J. Comput. Math. 93(3), 559–566 (2016)

    Article  MathSciNet  Google Scholar 

  18. Huang, R.: A qd-type algorithm for computing the generalized singular values of BF matrices with sign regularity to high relative accuracy. Math. Comput. 89, 229–252 (2020)

    Article  Google Scholar 

  19. Huang, R., Chu, D.-L.: Relative perturbation analysis for eigenvalues and singular values of totally nonpositive matrices. SIAM J. Matrix Anal. Appl. 38, 476–495 (2015)

    Article  MathSciNet  Google Scholar 

  20. Huang, R.: A periodic qd-type reduction for computing eigenvalues of structured matrix products to high relative accuracy. J. Sci. Comput. 75, 1229–1261 (2018)

    Article  MathSciNet  Google Scholar 

  21. Huang, R., Chu, D.-L.: Computing singular value decompositions of parameterized matrices with total nonpositivity to high relative accuracy. J. Sci. Comput. 71, 682–711 (2017)

    Article  MathSciNet  Google Scholar 

  22. Huang, R., Liu, J.-Z., Zhu, L.: Accurate solutions of diagonally dominant tridiagonal linear systems. BIT Nume. Math. 54, 711–727 (2014)

    Article  MathSciNet  Google Scholar 

  23. Alanelli, M., Hadjidimos, A.: A new iterative criterion for \(H\)-matrices: the reducible case. Linear Algebra Appl. 428, 2761–2777 (2008). https://doi.org/10.1016/j.laa.2007.12.020

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Jianzhou Liu & Lixin Zhou

  2. School of Science, Guilin University of Aerospace Technology, Guilin, 541004, Guangxi, People’s Republic of China

    Lixin Zhou

Authors
  1. Jianzhou Liu
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  2. Lixin Zhou
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Correspondence to Lixin Zhou.

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Communicated by Fatemeh Panjeh Ali Beik.

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The work was supported in part by National Natural Science Foundation of China (11971413), Guangxi Municipality Project for the Basic Ability Enhancement of Young and Middle-Aged Teachers (KY2016YB532, 2019KY0795).

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Liu, J., Zhou, L. Extended Irreducible Nekrasov Matrices as Subclasses of Irreducible H-Matrices. Bull. Iran. Math. Soc. 47, 1629–1640 (2021). https://doi.org/10.1007/s41980-020-00463-w

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  • DOI: https://doi.org/10.1007/s41980-020-00463-w

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