DocumentCode
933126
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
Volume
52
Issue
6
fYear
2007
fDate
6/1/2007 12:00:00 AM
Firstpage
1014
Lastpage
1026
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;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2007.899109
Filename
4237292
Link To Document