Condition number and backward errors of nonsymmetric algebraic Riccati equation

2014 ◽  
Vol 242 ◽  
pp. 716-728
Author(s):  
Lan-dong Liu ◽  
Shu-fang Xu
Keyword(s):  
Riccati Equation ◽  
Condition Number ◽  
Algebraic Riccati Equation ◽  
Nonsymmetric Algebraic Riccati Equation ◽  
Backward Errors

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.

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