Title :
A Control-Theoretic Approach to the Design of Zero Finding Numerical Methods
Author :
Bhaya, Amit ; Kaszkurewicz, Eugenius
Author_Institution :
Fed. Univ. of Rio de Janeiro, Rio de Janeiro
fDate :
6/1/2007 12:00:00 AM
Abstract :
In this paper, it is shown how standard iterative methods for solving linear and nonlinear equations can be designed from the point of view of control. Appropriate choices of control Lyapunov functions (CLFs) lead to both continuous and discrete-time versions of the Newton-Raphson and conjugate gradient algorithms as well as new variants.
Keywords :
Lyapunov methods; Newton-Raphson method; conjugate gradient methods; nonlinear equations; Newton-Raphson algorithms; conjugate gradient algorithms; control Lyapunov functions; iterative methods; nonlinear equations; zero finding numerical methods; Algorithm design and analysis; Character generation; Control systems; Guidelines; Iterative algorithms; Iterative methods; Lyapunov method; Nonlinear equations; PD control; Proportional control; Conjugate gradient (CG) algorithm; control Lyapunov functions (CLFs); iterative methods; proportional– integral–derivative control; zero finding methods;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2007.899109
