On the convergence of splittings for semidefinite linear systems |
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Authors: | Lijing Lin Ching-Wah Woo |
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Affiliation: | a Institute of Mathematics, School of Mathematical Science, Fudan University, Shanghai 200433, PR China b Key Laboratory of Nonlinear Science (Fudan University), Education of Ministry, PR China c Department of Mathematics, City University of Hong Kong, Hong Kong, PR China d Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, PR China e School of Applied Mathematics, Xinjiang University of Finance and Economics, Uramqi 830012, PR China |
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Abstract: | Recently, Lee et al. [Young-ju Lee, Jinbiao Wu, Jinchao Xu, Ludmil Zikatanov, On the convergence of iterative methods for semidefinite linear systems, SIAM J. Matrix Anal. Appl. 28 (2006) 634-641] introduce new criteria for the semi-convergence of general iterative methods for semidefinite linear systems based on matrix splitting. The new conditions generalize the classical notion of P-regularity introduced by Keller [H.B. Keller, On the solution of singular and semidefinite linear systems by iterations, SIAM J. Numer. Anal. 2 (1965) 281-290]. In view of their results, we consider here stipulations on a splitting A=M-N, which lead to fixed point systems such that, the iterative scheme converges to a weighted Moore-Penrose solution to the system Ax=b. Our results extend the result of Lee et al. to a more general case and we also show that it requires less restrictions on the splittings than Keller’s P-regularity condition to ensure the convergence of iterative scheme. |
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Keywords: | 65F10 65F15 |
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