Two-step modulus-based matrix splitting iteration methods for implicit complementarity problems

Abstract

In this paper, a class of two-step modulus-based matrix splitting (TMMS) iteration methods are proposed to solve the implicit complementarity problems. It is proved that the TMMS iteration methods are convergent under certain conditions when the system matrix is either a positive definite matrix or an H+-matrix. Two numerical examples are given to illustrate the effectiveness of the new proposed iteration methods. Numerical results show that the new proposed TMMS iteration methods have better performance than the existing modulus-based relaxation iteration methods for solving the implicit complementarity problems.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 11771225) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_1905).

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Correspondence to Yang Cao.

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Cao, Y., Wang, A. Two-step modulus-based matrix splitting iteration methods for implicit complementarity problems. Numer Algor 82, 1377–1394 (2019). https://doi.org/10.1007/s11075-019-00660-7

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Keywords

  • Implicit complementarity problem
  • Modulus method
  • Matrix splitting
  • Convergence

Mathematics Subject Classification (2010)

  • 65F10