scholarly journals Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory

2010 ◽  
Vol 432 (1) ◽  
pp. 283-291 ◽  
Author(s):  
Chun-Hua Guo ◽  
Wen-Wei Lin
Keyword(s):  
Iterative Methods ◽  
Convergence Rates ◽  
Transport Theory ◽  
Riccati Equations ◽  
Algebraic Riccati Equations

scholarly journals Two-Step Relaxation Newton Method for Nonsymmetric Algebraic Riccati Equations Arising from Transport Theory

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Shulin Wu ◽  
Chengming Huang
Keyword(s):  
Fixed Point ◽  
Positive Solution ◽  
Transport Theory ◽  
Riccati Equations ◽  
Monotone Convergence ◽  
Newton Methods ◽  
Vector Form ◽  
Algebraic Riccati Equations ◽  
Solution Sequence ◽  
Point Vector

We propose a new idea to construct an effective algorithm to compute the minimal positive solution of the nonsymmetric algebraic Riccati equations arising from transport theory. For a class of these equations, an important feature is that the minimal positive solution can be obtained by computing the minimal positive solution of a couple of fixed-point equations with vector form. Based on the fixed-point vector equations, we introduce a new algorithm, namely,two-step relaxation Newton, derived by combining two different relaxation Newton methods to compute the minimal positive solution. The monotone convergence of the solution sequence generated by this new algorithm is established. Numerical results are given to show the advantages of the new algorithm for the nonsymmetric algebraic Riccati equations in vector form.

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