Inexact Kleinman–Newton Method for Riccati Equations

Inexact Kleinman–Newton Method for Riccati Equations

In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity a...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2009-01, Vol.31 (2), p.272-288
Hauptverfasser: Feitzinger, F, Hylla, T, Sachs, E W
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Convergence
Iterative methods
Linear equations
Mathematical analysis
Mathematical models
Newton methods
Numerical analysis
Riccati equation
Solvers
Studies
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Zusammenfassung:In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results illustrate the efficiency of this method. [PUBLICATION ABSTRACT]
ISSN:0895-4798
1095-7162
DOI:10.1137/070700978