TY - JOUR
T1 - A Class of Asynchronous Matrix Multi-Splitting Multi-Parameter Relaxation Iterations
AU - Bai , Zhongzhi
AU - Wang , Deren
AU - Evans , D.J.
JO - Journal of Computational Mathematics
VL - 3
SP - 221
EP - 238
PY - 1998
DA - 1998/06
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9155.html
KW - System of linear equations, asynchronous iteration, matrix multisplitting, relaxation, convergence.
AB - <p style="text-align: justify;">A class of asynchronous matrix multi-splitting multi-parameter relaxation methods, including the asynchronous matrix multisplitting SAOR, SSOR and SGS methods as well as the known asynchronous matrix multisplitting AOR, SOR and GS methods, etc., is proposed for solving the large sparse systems of linear equations by making use of the principle of sufficiently using the delayed information. These new methods can greatly execute the parallel computational efficiency of the MIMD-systems, and are shown to be convergent when the coefficient matrices are $H$-matrices. Moreover, necessary and sufficient conditions ensuring the convergence of these methods are concluded for the case that the coefficient matrices are $L$-matrices.</p>