scholarly journals Low memory and low complexity iterative schemes for a nonsymmetric algebraic Riccati equation arising from transport theory

2013 ◽  
Vol 250 ◽  
pp. 175-189 ◽  
Author(s):  
Bo Yu ◽  
Dong-Hui Li ◽  
Ning Dong
Keyword(s):  
Riccati Equation ◽  
Transport Theory ◽  
Low Complexity ◽  
Algebraic Riccati Equation ◽  
Iterative Schemes ◽  
Nonsymmetric Algebraic Riccati Equation

Convergence Rates of a Class of Predictor-Corrector Iterations for the Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory

2017 ◽  
Vol 9 (4) ◽  
pp. 944-963 ◽  
Author(s):  
Ning Dong ◽  
Jicheng Jin ◽  
Bo Yu
Keyword(s):  
Riccati Equation ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Transport Theory ◽  
Algebraic Riccati Equation ◽  
Asymptotic Convergence ◽  
Comparison Theory ◽  
Nonsymmetric Algebraic Riccati Equation ◽  
Predictor Corrector ◽  
Asymptotic Convergence Rate

AbstractIn this paper, we analyse the convergence rates of several different predictor-corrector 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.

scholarly journals Different applications of RRE on nonsymmetric algebraic Riccati equation in transport theory

2019 ◽  
Vol 281 ◽  
pp. 05005
Author(s):  
Rola El Moallem ◽  
Hassane Sadok
Keyword(s):  
Riccati Equation ◽  
Transport Theory ◽  
Extrapolation Method ◽  
Algebraic Riccati Equation ◽  
Vector Sequence ◽  
Numerical Example ◽  
Vector Extrapolation ◽  
Nonsymmetric Algebraic Riccati Equation

This paper proposes three different ways of applying a vector extrapolation method to a slow converging vector sequence to accelerate the convergence. The solution of this vector sequence is used to solve an algebraic Riccati equation in transport theory. A numerical example is presented to compare the three applications.

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