• 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