Structured condition numbers and small sample condition estimation of symmetric algebraic Riccati equations
For researchers working on symmetric algebraic Riccati equations, this provides more accurate perturbation bounds and a practical estimation algorithm.
This paper derives upper bounds for structured condition numbers of symmetric algebraic Riccati equations, improving upon previous perturbation analysis. Numerical experiments show the condition numbers accurately estimate solution changes from data perturbations.
This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the analysis, the upper bounds for the structured normwise, mixed and componentwise condition numbers are derived. Due to the exploitation of the symmetry structure, our results are improvements of the 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 change in the solution caused by the perturbations on the data. Moreover, by applying the small sample condition estimation method, we propose a statistical algorithm for practically estimating the condition numbers of the symmetric algebraic Riccati equations.