TY - JOUR T1 - Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory AU - Dong , Ning AU - Jin , Jicheng AU - Yu , Bo JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 944 EP - 963 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1277 UR - https://global-sci.org/intro/article_detail/aamm/12184.html KW - Convergence rate, predictor-corrector iterations, nonsymmetric algebraic Riccati equation, regular splitting. AB -

In this paper, we analyse the convergence rates of several different predictor-corrector iterations for computing the minimal positive solution of the nonsymmetric algebraic Riccati equation arising in transport theory. We have shown theoretically that the new predictor-corrector iteration given in [Numer. Linear Algebra Appl., 21 (2014), pp. 761–780] will converge no faster than the simple predictor-corrector iteration and the nonlinear block Jacobi predictor-corrector iteration. Moreover, the last two have the same asymptotic convergence rate with the nonlinear block Gauss-Seidel iteration given in [SIAM J. Sci. Comput., 30 (2008), pp. 804–818]. Preliminary numerical experiments have been reported for the validation of the developed comparison theory.