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2022, Volume 7, Issue 6: 10994-11014. doi: 10.3934/math.2022614
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Research article

A general modulus-based matrix splitting method for quasi-complementarity problem

  • 1.
    School of Information Science and Technology, Nantong University, Nantong 226019, China
  • 2.
    School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China
  • 3.
    School of Sciences, Nantong University, Nantong 226019, China
  • Received: 22 December 2021 Revised: 14 March 2022 Accepted: 28 March 2022 Published: 06 April 2022

  • MSC : 65F10

  • For large sparse quasi-complementarity problem (QCP), Wu and Guo [35] recently studied a modulus-based matrix splitting (MMS) iteration method, which belongs to a class of inner-outer iteration methods. In order to improve the convergence rate of the inner iteration so as to get fast convergence rate of the outer iteration, a general MMS (GMMS) iteration method is proposed in this paper. Convergence analyses on the GMMS method are studied in detail when the system matrix is either an $ H_{+} $-matrix or a positive definite matrix. In the case of $ H_{+} $-matrix, weaker convergence condition of the GMMS iteration method is obtained. Finally, two numerical experiments are conducted and the results indicate that the new proposed GMMS method achieves a better performance than the MMS iteration method.

    Citation: Chen-Can Zhou, Qin-Qin Shen, Geng-Chen Yang, Quan Shi. A general modulus-based matrix splitting method for quasi-complementarity problem[J]. AIMS Mathematics, 2022, 7(6): 10994-11014. doi: 10.3934/math.2022614

    Related Papers:

  • For large sparse quasi-complementarity problem (QCP), Wu and Guo [35] recently studied a modulus-based matrix splitting (MMS) iteration method, which belongs to a class of inner-outer iteration methods. In order to improve the convergence rate of the inner iteration so as to get fast convergence rate of the outer iteration, a general MMS (GMMS) iteration method is proposed in this paper. Convergence analyses on the GMMS method are studied in detail when the system matrix is either an $ H_{+} $-matrix or a positive definite matrix. In the case of $ H_{+} $-matrix, weaker convergence condition of the GMMS iteration method is obtained. Finally, two numerical experiments are conducted and the results indicate that the new proposed GMMS method achieves a better performance than the MMS iteration method.


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