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Analysis and modificaton of Newton's method for algebraic Riccati equations
Author(s):
Chun-Hua
Guo;
Peter
Lancaster.
Journal:
Math. Comp.
67
(1998),
1089-1105.
MSC (1991):
Primary 65H10;
Secondary 15A24, 93B40
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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:
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.
Copyright of article:
Copyright
1998,
American Mathematical Society
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