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 & Bo Yu

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

Published online: 2018-05

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  • Abstract

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.

  • Keywords

Convergence rate, predictor-corrector iterations, nonsymmetric algebraic Riccati equation, regular splitting.

  • AMS Subject Headings

65F50, 15A24

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-944, author = {Ning Dong , and Jicheng Jin , and Yu , Bo}, title = {Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {4}, pages = {944--963}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1277}, url = {http://global-sci.org/intro/article_detail/aamm/12184.html} }
TY - JOUR T1 - Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory AU - Ning Dong , AU - Jicheng Jin , 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.

Ning Dong, Jicheng Jin & Bo Yu. (2020). 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. 9 (4). 944-963. doi:10.4208/aamm.2015.m1277
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