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 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.

  • 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 = {}, 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 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.

}, 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 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 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.

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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