Open AccessA general modulus-based matrix splitting method for quasi-complementarity problem
Author(s) -
Chen–Can Zhou,
Qin-Qin Shen,
Gengchen Yang,
Quan Shi
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022614
Subject(s) - mathematics , rate of convergence , matrix (chemical analysis) , complementarity (molecular biology) , convergence (economics) , power iteration , iterative method , positive definite matrix , algorithm , computer science , physics , materials science , key (lock) , eigenvalues and eigenvectors , computer security , quantum mechanics , economics , composite material , genetics , biology , economic growth
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.