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2013, 3(2): 261-270. doi: 10.3934/naco.2013.3.261

## The stationary iterations revisited

 1 Department of Computer Science, Fitchburg State University, Fitchburg, MA 01420, United States 2 Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China 3 School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China

Received  February 2012 Revised  January 2013 Published  April 2013

In this paper, we first present a necessary and sufficient conditions for the weakly and strongly convergence of the general stationary iterations $x^{(k+1)} = T x^{(k)} +c$ with initial iteration matrix $T$ and vectors $c$ and $x^{(0)}$. Then we apply these general results and present convergence conditions for the stationary iterations for solving singular linear system $A x = b$. We show that our convergence conditions are weaker and more general than the known results.
Citation: Xuzhou Chen, Xinghua Shi, Yimin Wei. The stationary iterations revisited. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 261-270. doi: 10.3934/naco.2013.3.261
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