caa a22 4500 467988870 CHVBK 20180323112539.0 cr unu---uuuuu 170328e19900901xx s 000 0 eng 10.1007/BF02551369 doi (NATIONALLICENCE)springer-10.1007/BF02551369 Error bounds for Newton refinement of solutions to algebraic riccati equations [Elektronische Daten] [Charles Kenney, Alan Laub, Matt Wette] Recent error bounds derived from the Schur method of solving algebraic Riccati equations (ARE) complement residual error bounds associated with Newton refinement of approximate solutions. These approaches to the problem of error estimation not only work well together but also represent the first computable error bounds for the solution of Riccati equations. In this paper the closed-loop Lyapunov operator is seen to be central to the question of whether Newton refinement will improve an approximate solution (region of convergence), as well as providing a means of bounding the actual error in terms of the residual error. In turn, both of these issues are related to the condition of the ARE and the damping of the associated closed-loop dynamical system. Numerical results are given for seven problems taken from the literature. Springer-Verlag New York Inc., 1990 Riccati equations nationallicence Newton's method nationallicence Iterative refinement nationallicence Lyapunov operator nationallicence Error bounds nationallicence Residual bounds nationallicence Kenney Charles Department of Electrical and Computer Engineering, University of California, 93106, Santa Barbara, California, USA aut Laub Alan Department of Electrical and Computer Engineering, University of California, 93106, Santa Barbara, California, USA aut Wette Matt Department of Electrical and Computer Engineering, University of California, 93106, Santa Barbara, California, USA aut Mathematics of Control, Signals and Systems Springer-Verlag 3/3(1990-09-01), 211-224 0932-4194 3:3<211 1990 3 498 https://doi.org/10.1007/BF02551369 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02551369 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kenney Charles Department of Electrical and Computer Engineering, University of California, 93106, Santa Barbara, California, USA aut NATIONALLICENCE 700 1- Laub Alan Department of Electrical and Computer Engineering, University of California, 93106, Santa Barbara, California, USA aut NATIONALLICENCE 700 1- Wette Matt Department of Electrical and Computer Engineering, University of California, 93106, Santa Barbara, California, USA aut NATIONALLICENCE 773 0- Mathematics of Control, Signals and Systems Springer-Verlag 3/3(1990-09-01), 211-224 0932-4194 3:3<211 1990 3 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer