On the convergence of the discretized parallel chaotic waveform relaxation method. (Q1412577)

The authors discuss three parallel chaotic algorithms based on some models previously studied by \textit{R. Bru, L. Elsner}, and \textit{M. Neumman} [Linear Algebra Appl. 103, 175--192 (1988; Zbl 0645.65018)], \textit{P. E. Kloeden} and \textit{D. J. Yuan} [Bull. Aust. Math. Soc. 50, No.~1, 167--176 (1994; Zbl 0815.65045)], and \textit{Y. Song} and \textit{D. Yuan} [On the convergence of relaxed parallel chaotic interactions for \(H\)-matrix, Int. J. Comp. Math. 52, 195--209 (1994)], for solving systems of linear ordinary differential equations. They use different assumptions on the coefficient matrix and its multiplication to obtain sufficient conditions for the convergence of the algorithms. Convergence speed comparisons for different algorithms are also given.