Perturbation analysis and condition numbers of rational Riccati equations

2021 ◽  
Vol 6 (1) ◽  
pp. 25-49
Author(s):  
Peter Chang-Yi Weng ◽  
Frederick Kin Hing Phoa
Keyword(s):  
Perturbation Analysis ◽  
Riccati Equations ◽  
Condition Numbers

Perturbation analysis and condition numbers of symmetric algebraic Riccati equations

Automatica ◽  
2009 ◽  
Vol 45 (4) ◽  
pp. 1005-1011 ◽  
Author(s):  
Liangmin Zhou ◽  
Yiqin Lin ◽  
Yimin Wei ◽  
Sanzheng Qiao
Keyword(s):  
Perturbation Analysis ◽  
Riccati Equations ◽  
Condition Numbers ◽  
Algebraic Riccati Equations

Perturbation Analysis of the Continuous and Discrete Matrix Riccati Equations

1986 ◽  
Author(s):  
M.M. Konstantinov ◽  
P.Hr. Petkov ◽  
N.D. Christov
Keyword(s):  
Perturbation Analysis ◽  
Riccati Equations

scholarly journals The generalized condition numbers of bounded linear operators in Banach spaces

2004 ◽  
Vol 76 (2) ◽  
pp. 281-290 ◽  
Author(s):  
Guoliang Chen ◽  
Yimin Wei ◽  
Yifeng Xue
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Perturbation Analysis ◽  
Bounded Linear Operator ◽  
Linear Operators ◽  
Condition Numbers ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Ill Posed ◽  
Linear Operator Equations

AbstractFor any bounded linear operator A in a Banach space, two generalized condition numbers, k(A) and k(A) are defined in this paper. These condition numbers may be applied to the perturbation analysis for the solution of ill-posed differential equations and bounded linear operator equations in infinite dimensional Banach spaces. Different expressions for the two generalized condition numbers are discussed in this paper and applied to the perturbation analysis of the operator equation.

Perturbation analysis and condition numbers of scaled total least squares problems

2009 ◽  
Vol 51 (3) ◽  
pp. 381-399 ◽  
Author(s):  
Liangmin Zhou ◽  
Lijing Lin ◽  
Yimin Wei ◽  
Sanzheng Qiao
Keyword(s):  
Least Squares ◽  
Perturbation Analysis ◽  
Total Least Squares ◽  
Condition Numbers ◽  
Least Squares Problems

scholarly journals Calibrating linear continuous-time dynamical systems via perturbation analysis

Filomat ◽  
2018 ◽  
Vol 32 (5) ◽  
pp. 1909-1915
Author(s):  
Peter Weng ◽  
Frederick Phoa
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Perturbation Analysis ◽  
Continuous Time ◽  
Riccati Equations ◽  
Linear Dynamical Systems ◽  
The Matrix ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Time Linear

This work considered the continuous-time linear dynamical systems described by the matrix differential equations, and aimed at studying the perturbation analysis via solving perturbed linear dynamical systems. In specific, we solved Riccati differential equations and continuous-time algebraic Riccati equations with finite and infinite times respectively. Moreover, we stated some assumptions on the existence and uniqueness of the solutions of the perturbed Riccati equations. Similar techniques were applied to the discrete-time linear dynamical systems. Two numerical examples illustrated the efficiency and accuracy.

PERTURBATION ANALYSIS OF COUPLED MATRIX RICCATI EQUATIONS

2002 ◽  
Vol 35 (1) ◽  
pp. 307-312
Author(s):  
Mihail Konstantinov ◽  
Vera Angelova ◽  
Petko Petkov ◽  
Dawei Gu ◽  
Vassilios Tsachouridis
Keyword(s):  
Perturbation Analysis ◽  
Riccati Equations

Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems

2010 ◽  
Vol 18 (1) ◽  
pp. 87-103 ◽  
Author(s):  
Delin Chu ◽  
Lijing Lin ◽  
Roger C. E. Tan ◽  
Yimin Wei
Keyword(s):  
Tikhonov Regularization ◽  
Perturbation Analysis ◽  
Condition Numbers ◽  
Ill Posed
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