Abstract
In this paper, we present some novel observations for the semidefinite linear complementarity problems, abbreviated as SDLCPs. Based on these new results, we establish the modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently SDLCP as an implicit fixed-point matrix equation. The convergence of the proposed modulus-based matrix splitting iteration methods has been analyzed. Numerical experiments have shown that the modulus-based iteration methods are effective for solving SDLCPs.
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Acknowledgments
The author would like to express the great thankfulness to the referees for the comments and constructive suggestions very much, which are valuable in improving the quality of the original paper.
Funding
This work was financially supported by National Natural Science Foundation of China (Nos. 11901098 and U1839207) and National Key Research and Development Program of China (Nos. 2018YFC1504200 and 2017YFC0601505).
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Ke, YF. Convergence analysis on matrix splitting iteration algorithm for semidefinite linear complementarity problems. Numer Algor 86, 257–279 (2021). https://doi.org/10.1007/s11075-020-00888-8
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DOI: https://doi.org/10.1007/s11075-020-00888-8
Keywords
- Semidefinite linear complementarity problems
- Matrix splitting
- Iteration methods
- Sylvester-type matrix equation
- Lyapunov matrix equation
- Stein matrix equation