DocumentCode
2631913
Title
Iterative methods as dynamical systems with feedback control
Author
Bhaya, Amit ; Kaszkurewicz, Eugenius
Author_Institution
Dept. of Electr. Eng., Fed. Univ. of Rio de Janeiro, Brazil
Volume
3
fYear
2003
fDate
9-12 Dec. 2003
Firstpage
2374
Abstract
It is shown how standard iterative methods for solving linear and nonlinear equations can be approached from the point of view of control. Appropriate choices of control Lyapunov functions lead to both continuous and discrete-time versions of the well-known Newton-Raphson and conjugate gradient algorithms as well as their common variants. Insights into these algorithms that result from the control approach are discussed.
Keywords
Lyapunov methods; Newton-Raphson method; conjugate gradient methods; continuous time systems; discrete time systems; feedback; nonlinear equations; time-varying systems; Lyapunov functions; Newton-Raphson algorithm; conjugate gradient algorithm; continuous time system; discrete-time system; dynamical systems; feedback control; iterative methods; linear equations; nonlinear equations; Algorithm design and analysis; Computer aided software engineering; Control theory; Feedback control; Iterative algorithms; Iterative methods; Nonlinear control systems; Nonlinear equations; Numerical analysis; Robustness;
fLanguage
English
Publisher
ieee
Conference_Titel
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
ISSN
0191-2216
Print_ISBN
0-7803-7924-1
Type
conf
DOI
10.1109/CDC.2003.1272974
Filename
1272974
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