Volume 10, Issue 6
Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation

Bo Tang, Yunqing Huang & Ning Dong

Adv. Appl. Math. Mech., 10 (2018), pp. 1327-1343.

Published online: 2018-09

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  • Abstract

We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix. It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm (SDA) with the shift-and-shrink transformation or the generalized Cayley transformation. In this paper, we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases. Meanwhile, the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined. Moreover, the convergence result and the comparison theorem on convergent rate are established. Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.

  • Keywords

Shift-and-shrink transformation generalized Cayley transformation doubling algorithm nonsymmetric algebraic Riccati equation.

  • AMS Subject Headings

65F50 15A24

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-1327, author = {Bo Tang, Yunqing Huang and Ning Dong}, title = {Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {6}, pages = {1327--1343}, abstract = {

We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix. It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm (SDA) with the shift-and-shrink transformation or the generalized Cayley transformation. In this paper, we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases. Meanwhile, the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined. Moreover, the convergence result and the comparison theorem on convergent rate are established. Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0012}, url = {http://global-sci.org/intro/article_detail/aamm/12713.html} }
TY - JOUR T1 - Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation AU - Bo Tang, Yunqing Huang & Ning Dong JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1327 EP - 1343 PY - 2018 DA - 2018/09 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2018-0012 UR - https://global-sci.org/intro/aamm/12713.html KW - Shift-and-shrink transformation KW - generalized Cayley transformation KW - doubling algorithm KW - nonsymmetric algebraic Riccati equation. AB -

We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix. It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm (SDA) with the shift-and-shrink transformation or the generalized Cayley transformation. In this paper, we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases. Meanwhile, the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined. Moreover, the convergence result and the comparison theorem on convergent rate are established. Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.

Bo Tang, Yunqing Huang & Ning Dong. (1970). Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation. Advances in Applied Mathematics and Mechanics. 10 (6). 1327-1343. doi:10.4208/aamm.OA-2018-0012
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