Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we analyse the convergence rates of several different predictor-correctoriterations for computing the minimal positive solution of the nonsymmetricalgebraic Riccati equation arising in transport theory. We have shown theoreticallythat 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 iterationand the nonlinear block Jacobi predictor-corrector iteration. Moreover, the lasttwo have the same asymptotic convergence rate with the nonlinear block Gauss-Seideliteration given in [SIAM J. Sci. Comput., 30 (2008), pp. 804–818]. Preliminary numericalexperiments have been reported for the validation of the developed comparisontheory.