TY - JOUR
T1 - Parallel Quasi-Chebyshev Acceleration to Nonoverlapping Multisplitting Iterative Methods Based on Optimization
JO - Journal of Computational Mathematics
VL - 3
SP - 284
EP - 296
PY - 2014
DA - 2014/06
SN - 32
DO - http://doi.org/10.4208/jcm.1401-CR1
UR - https://global-sci.org/intro/article_detail/jcm/9886.html
KW - Parallel quasi-Chebyshev acceleration, Nonoverlapping multisplitting iterative
method, Convergence, Optimization.
AB - <p style="text-align: justify;">In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an $H$-matrix or a symmetric positive definite matrix. First, $m$ parallel iterations are implemented in $m$ different processors. Second, based on $l_1$-norm or $l_2$-norm, the $m$ optimization models are parallelly treated in $m$ different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numerical examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.</p>