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New Alternately Linearized Implicit Iteration for M-Matrix Algebraic Riccati Equations

New Alternately Linearized Implicit Iteration for M-Matrix Algebraic Riccati Equations
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Year:    2017

Author:    Jinrui Guan, Linzhang Lu

Journal of Mathematical Study, Vol. 50 (2017), Iss. 1 : pp. 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 NALI method is more efficient than the ALI method in some cases.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v50n1.17.04

Journal of Mathematical Study, Vol. 50 (2017), Iss. 1 : pp. 54–64

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    M-matrix algebraic Riccati equation M-matrix ALI iteration method.

Author Details

Jinrui Guan

Linzhang Lu

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