Virginia TechBurns, John A.Sachs, Ekkehard W.Zietsman, Lizette2014-05-282014-05-282008Burns, J. A.; Sachs, E. W.; Zietsman, L., "Mesh independence of Kleinman-Newton iterations for Riccati equations in Hilbert space," SIAM J. Control Optim., 47(5), 2663-2692, (2008). DOI: 10.1137/0606539620363-0129http://hdl.handle.net/10919/48137In this paper we consider the convergence of the infinite dimensional version of the Kleinman-Newton algorithm for solving the algebraic Riccati operator equation associated with the linear quadratic regulator problem in a Hilbert space. We establish mesh independence for this algorithm and apply the result to systems governed by delay equations. Numerical examples are presented to illustrate the results.application/pdfen-USIn Copyrightriccatikleinman-newtonmesh independencepartial-differential-equationsspline approximationsretarded-systemsoperatorsdelaysidentificationconvergencesensitivitystabilityprincipleautomation & control systemsmathematics, appliedArticle - Refereedhttp://epubs.siam.org/doi/abs/10.1137/060653962https://doi.org/10.1137/060653962