A general modulus-based matrix splitting method for quasi-complementarity problem
For large sparse quasi-complementarity problem (QCP), Wu and Guo <sup>[<xref ref-type="bibr" rid="b35">35</xref>]</sup> recently studied a modulus-based matrix splitting (MMS) iteration method, which belongs to a class of inner-outer iteration methods. In...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-04-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022614?viewType=HTML |
| _version_ | 1828845704544518144 |
|---|---|
| author | Chen-Can Zhou Qin-Qin Shen Geng-Chen Yang Quan Shi |
| author_facet | Chen-Can Zhou Qin-Qin Shen Geng-Chen Yang Quan Shi |
| author_sort | Chen-Can Zhou |
| collection | DOAJ |
| description | For large sparse quasi-complementarity problem (QCP), Wu and Guo <sup>[<xref ref-type="bibr" rid="b35">35</xref>]</sup> 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. |
| first_indexed | 2024-12-12T21:34:07Z |
| format | Article |
| id | doaj.art-f4f90e133edb467ca5d214d4f091ea72 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T21:34:07Z |
| publishDate | 2022-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f4f90e133edb467ca5d214d4f091ea722022-12-22T00:11:15ZengAIMS PressAIMS Mathematics2473-69882022-04-0176109941101410.3934/math.2022614A general modulus-based matrix splitting method for quasi-complementarity problemChen-Can Zhou0Qin-Qin Shen1Geng-Chen Yang2Quan Shi31. School of Information Science and Technology, Nantong University, Nantong 226019, China 2. School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China2. School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China3. School of Sciences, Nantong University, Nantong 226019, China2. School of Transportation and Civil Engineering, Nantong University, Nantong 226019, ChinaFor large sparse quasi-complementarity problem (QCP), Wu and Guo <sup>[<xref ref-type="bibr" rid="b35">35</xref>]</sup> 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.https://www.aimspress.com/article/doi/10.3934/math.2022614?viewType=HTMLquasi-complementarity problemmodulus-based iteration methodmatrix splittingconvergence |
| spellingShingle | Chen-Can Zhou Qin-Qin Shen Geng-Chen Yang Quan Shi A general modulus-based matrix splitting method for quasi-complementarity problem AIMS Mathematics quasi-complementarity problem modulus-based iteration method matrix splitting convergence |
| title | A general modulus-based matrix splitting method for quasi-complementarity problem |
| title_full | A general modulus-based matrix splitting method for quasi-complementarity problem |
| title_fullStr | A general modulus-based matrix splitting method for quasi-complementarity problem |
| title_full_unstemmed | A general modulus-based matrix splitting method for quasi-complementarity problem |
| title_short | A general modulus-based matrix splitting method for quasi-complementarity problem |
| title_sort | general modulus based matrix splitting method for quasi complementarity problem |
| topic | quasi-complementarity problem modulus-based iteration method matrix splitting convergence |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022614?viewType=HTML |
| work_keys_str_mv | AT chencanzhou ageneralmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem AT qinqinshen ageneralmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem AT gengchenyang ageneralmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem AT quanshi ageneralmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem AT chencanzhou generalmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem AT qinqinshen generalmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem AT gengchenyang generalmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem AT quanshi generalmodulusbasedmatrixsplittingmethodforquasicomplementarityproblem |