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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Analysis and modificaton of Newton's method
for algebraic Riccati equations


Authors: Chun-Hua Guo and Peter Lancaster
Journal: Math. Comp. 67 (1998), 1089-1105
MSC (1991): Primary 65H10; Secondary 15A24, 93B40
MathSciNet review: 1459388
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Abstract | References | Similar Articles | Additional Information

Abstract: When Newton's method is applied to find the maximal symmetric solution of an algebraic Riccati equation, convergence can be guaranteed under moderate conditions. In particular, the initial guess need not be close to the solution. The convergence is quadratic if the Fréchet derivative is invertible at the solution. In this paper we examine the behaviour of the Newton iteration when the derivative is not invertible at the solution. We find that a simple modification can improve the performance of the Newton iteration dramatically.


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Additional Information

Chun-Hua Guo
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Email: guo@math.ucalgary.ca

Peter Lancaster
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Email: lancaste@math.ucalgary.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-98-00947-8
PII: S 0025-5718(98)00947-8
Received by editor(s): February 18, 1997
Additional Notes: Research supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 1998 American Mathematical Society