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The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications

Author

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  • Liu, Jianzhou
  • Zhang, Juan
  • Zhou, Lixin
  • Tu, Gen

Abstract

In this paper, we estimate the Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices. As an application, we offer new bounds of the determinant for several special matrices, which improve the related results in certain case. Further, we give an estimation on the infinity norm bounds for the inverse of Schur complement of Nekrasov matrices. Finally, we introduce new methods called Schur-based super relaxation iteration (SSSOR) method and Schur-based conjugate gradient (SCG) method to solve the linear equation by reducing order. The numerical examples illustrate the effectiveness of the derived result.

Suggested Citation

  • Liu, Jianzhou & Zhang, Juan & Zhou, Lixin & Tu, Gen, 2018. "The Nekrasov diagonally dominant degree on the Schur complement of Nekrasov matrices and its applications," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 251-263.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:251-263
    DOI: 10.1016/j.amc.2017.09.032
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    Cited by:

    1. Orera, H. & Peña, J.M., 2019. "Infinity norm bounds for the inverse of Nekrasov matrices using scaling matrices," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 119-127.
    2. Xin Li & Mei Qin, 2019. "Criteria for H-Matrices Based on γ−Diagonally Dominant Matrix," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(6), pages 1-1, December.

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