Structured Condition Numbers of Symmetric Algebraic Riccati Equations

This paper presents a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, structured normwise, componentwise, and mixed condition numbers are defined and their explicit expressions are derived. Due to the exploitation of the symmetry structure, our results are improvements of previous work on the perturbation analysis and condition numbers of the symmetric algebraic Riccati equations. Our preliminary numerical experiments demonstrate that our condition numbers provide accurate estimates for the errors in the solution caused by the perturbations on the data.