caa a22 4500 445852429 CHVBK 20180317145417.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s11227-010-0400-8 doi (NATIONALLICENCE)springer-10.1007/s11227-010-0400-8 Condition for relaxed Monte Carlo method of solving systems of linear equations [Elektronische Daten] [Guoming Lai, Xiaola Lin] In this paper, we point out the limitation of the paper entitled "Solving Systems of Linear Equations with Relaxed Monte Carlo Method” published in this journal (Tan in J. Supercomput. 22:113-123, 2002). We argue that the relaxed Monte Carlo method presented in Sect.7 of the paper is only correct under the condition that the coefficient matrix A must be diagonal dominate. However, for nondiagonal dominate case; the corresponding Neumann series may diverge, which would lead to infinite loop when simulating the iterative Monte Carlo algorithm. In this paper, we first prove that only for the diagonal dominate matrix, the corresponding von Neumann series can converge, and the Monte Carlo algorithm can be relaxed. Therefore, it is not true for nondiagonal dominate matrix, no matter the relaxed parameter γ is a single value or a set of values. We then present and analyze the numerical experiment results to verify our arguments. Springer Science+Business Media, LLC, 2010 Monte Carlo methods nationallicence Relaxed Monte Carlo method nationallicence Diagonal dominate matrix nationallicence Lai Guoming School of Information Science and Technology, Sun Yat-sen University, 510275, Guangzhou, China aut Lin Xiaola School of Information Science and Technology, Sun Yat-sen University, 510275, Guangzhou, China aut The Journal of Supercomputing Springer US; http://www.springer-ny.com 57/3(2011-09-01), 256-264 0920-8542 57:3<256 2011 57 11227 https://doi.org/10.1007/s11227-010-0400-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11227-010-0400-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lai Guoming School of Information Science and Technology, Sun Yat-sen University, 510275, Guangzhou, China aut NATIONALLICENCE 700 1- Lin Xiaola School of Information Science and Technology, Sun Yat-sen University, 510275, Guangzhou, China aut NATIONALLICENCE 773 0- The Journal of Supercomputing Springer US; http://www.springer-ny.com 57/3(2011-09-01), 256-264 0920-8542 57:3<256 2011 57 11227 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer