On the semiconvergence of extrapolated iterative methods for singular linear systems
The solution of square linear systems with singular coefficient matrix by extrapolated iterative methods is considered. Sufficient and necessary conditions for the semiconvergence of the extrapolated iterative methods are presented, extending the extrapolation theorem given by \textit{Z. Cao} [Appl. Numer. Anal. 27, 203-209 (1998; Zbl 0927.65052)] and improving the corresponding results by \textit{Y. Song} [J. Comput. Appl. Math. 106, 117-129 (1999; Zbl 0930.65033)]. In particular, the semiconvergence of the (generalized, block) Jacobi-overrelaxation (JOR) and (generalized, block) accelerated overrelaxation (AOR) methods are investigated. Five examples illustrate and show the limits of the theoretical results.
scientific article; zbMATH DE number 1879017