Condition number and backward errors of nonsymmetric algebraic Riccati equation

Liu, Landong; Xu, Shengyuan

doi:10.1016/j.amc.2014.06.036

Cited by 1 publication

(2 citation statements)

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“…Consider the NDRE (1), constructed according to the rules given in [15]. This scheme is used in [10] to analyze the effectiveness of mixed and componentwise condition numbers, and in [11], to illustrate the validity of a condition number and backward errors of nonsymmetric algebraic Riccati equation.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…To estimate the actual error in the computed solution, it is important to find a bound of the error in the computed solution in terms of the perturbations in the data. Perturbation analysis of the nonsymmetric algebraic Riccati equation is given in [8], normwise, mixed and componentwise condition numbers, as well as residual bounds are proposed in [9][10][11]. To the best of our knowledge, the sensitivity and the conditioning of the NDRE are not yet analyzed.This work has two goals.…”

Section: Introduction and Notationsmentioning

confidence: 99%

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Sensitivity of the Solution to Nonsymmetric Differential Matrix Riccati Equation

2021

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Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to the nonsymmetric case. Applying the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principle, two perturbation bounds are derived: the first one is based on the integral form of the solution and the second one considers the equivalent solution to the initial value problem of the associated differential system. The first bound is derived for the nonsymmetric differential Riccati equation in its general form. The perturbation bound based on the sensitivity analysis of the associated linear differential system is formulated for the low-dimensional approximate solution to the large-scale nonsymmetric differential Riccati equation. The two bounds exploit the existing sensitivity estimates for the matrix exponential and are alternative.

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Section: Numerical Examplesmentioning

confidence: 99%