TY  - JOUR
T1  - On numerical behavior of matrix splitting iteration methods
A1  - Bai, Zhong-Zhi
A1  - Rozložník, Miroslav
JA  - SIAM Journal on Numerical Analysis (SINUM)
Y1  - 2015
VL  - 53
IS  - 4
SP  - 1116
EP  - 1137
M2  - doi: 10.1137/140987936
KW  - backward error
KW  - convergence rate
KW  - matrix splitting
KW  - rounding error analysis
KW  - stationary iteration method
N2  - We study numerical behavior of stationary single- or two-step matrix splitting iteration methods for solving large sparse systems of linear equations. We show that inexact solutions of inner linear systems associated with the matrix splittings may considerably influence the convergenceand the ac- curacy of the approximate solutions computed in finite precision arithmetic. For a general stationary matrix splitting iteration method, we analyze two mathematically equivalent implementations and find the corresponding componentwise or normwise forward or backward stable implementation.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 18
M1  - Preprint ID = NCMM/2014/18
ER  -