Volume 50, Issue 1
New Alternately Linearized Implicit Iteration for M-matrix Algebraic Riccati Equations

Jinrui Guan & Linzhang Lu

J. Math. Study, 50 (2017), pp. 54-64.

Published online: 2017-03

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  • Abstract

Research on the theories and the efficient numerical methods of M-matrix algebraic Riccati equation (MARE) has become a hot topic in recent years due to its broad applications. In this paper, based on the alternately linearized implicit iteration method (ALI) [Z.-Z. Bai et al., Numer. Linear Algebra Appl., 13(2006), 655-674.], we propose a new alternately linearized implicit iteration method (NALI) for computing the minimal nonnegative solution of M-matrix algebraic Riccati equation. Convergence of the NALI method is proved by choosing proper parameters for the MARE associated with nonsingular M-matrix or irreducible singular M-matrix. Theoretical analysis and numerical experiments show that the NALImethod is more efficient than the ALI method in some cases.

  • Keywords

M-matrix algebraic Riccati equation M-matrix ALI iteration method

  • AMS Subject Headings

15A24, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

guanjinrui2012@163.com (Jinrui Guan)

llz@gznu.edu.cn (Linzhang Lu)

  • BibTex
  • RIS
  • TXT
@Article{JMS-50-54, author = {Guan , Jinrui and Lu , Linzhang}, title = {New Alternately Linearized Implicit Iteration for M-matrix Algebraic Riccati Equations}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {1}, pages = {54--64}, abstract = {

Research on the theories and the efficient numerical methods of M-matrix algebraic Riccati equation (MARE) has become a hot topic in recent years due to its broad applications. In this paper, based on the alternately linearized implicit iteration method (ALI) [Z.-Z. Bai et al., Numer. Linear Algebra Appl., 13(2006), 655-674.], we propose a new alternately linearized implicit iteration method (NALI) for computing the minimal nonnegative solution of M-matrix algebraic Riccati equation. Convergence of the NALI method is proved by choosing proper parameters for the MARE associated with nonsingular M-matrix or irreducible singular M-matrix. Theoretical analysis and numerical experiments show that the NALImethod is more efficient than the ALI method in some cases.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n1.17.04}, url = {http://global-sci.org/intro/article_detail/jms/979.html} }
TY - JOUR T1 - New Alternately Linearized Implicit Iteration for M-matrix Algebraic Riccati Equations AU - Guan , Jinrui AU - Lu , Linzhang JO - Journal of Mathematical Study VL - 1 SP - 54 EP - 64 PY - 2017 DA - 2017/03 SN - 50 DO - http://doi.org/10.4208/jms.v50n1.17.04 UR - https://global-sci.org/intro/article_detail/jms/979.html KW - M-matrix algebraic Riccati equation KW - M-matrix KW - ALI iteration method AB -

Research on the theories and the efficient numerical methods of M-matrix algebraic Riccati equation (MARE) has become a hot topic in recent years due to its broad applications. In this paper, based on the alternately linearized implicit iteration method (ALI) [Z.-Z. Bai et al., Numer. Linear Algebra Appl., 13(2006), 655-674.], we propose a new alternately linearized implicit iteration method (NALI) for computing the minimal nonnegative solution of M-matrix algebraic Riccati equation. Convergence of the NALI method is proved by choosing proper parameters for the MARE associated with nonsingular M-matrix or irreducible singular M-matrix. Theoretical analysis and numerical experiments show that the NALImethod is more efficient than the ALI method in some cases.

Jinrui Guan & Linzhang Lu. (2019). New Alternately Linearized Implicit Iteration for M-matrix Algebraic Riccati Equations. Journal of Mathematical Study. 50 (1). 54-64. doi:10.4208/jms.v50n1.17.04
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