Volume 9, Issue 4
Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory

Ning Dong ,  Jicheng Jin and Bo Yu


Adv. Appl. Math. Mech., 9 (2017), pp. 944-963.

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  • Abstract

In this paper, we analyse the convergence rates of several different predictorcorrector 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.

  • History

Published online: 2018-05

  • AMS Subject Headings

65F50, 15A24

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