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
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;
Conference_Titel :
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
Print_ISBN :
0-7803-7924-1
DOI :
10.1109/CDC.2003.1272974
