The Computational Complexity of Iterative Methods for Systems of Nonlinear Equations

  • Richard Brent
Part of the The IBM Research Symposia Series book series (IRSS)


Suppose that an iterative method M generates successive approximations \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}\to {X} _0 ,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}\to {X} _1 , \ldots\) to a solution \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}\to {X} *\) of the system
$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}\to {f} \left( {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}\to {x} } \right) = Q$$
of n nonlinear equations in n unknowns.


Function Evaluation Iterative Method Nonlinear Equation Successive Approximation Order Unity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • Richard Brent
    • 1
  1. 1.Mathematical Sciences DepartmentIBM Thomas J. Watson Research CenterYorktown HeightsUSA

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