We study a continuous analogue of Newton method for solving the nonlinear equation
where holomorphic function and . It is proved that this method converges, to the solution for each initial data , if and only if is a star-like function with respect to either an interior or a boundary point. Our study is based on the theory of one parameter continuous semigroups. It enables us to consider convergence in the case of an interior as well as a boundary location of the solution by the same approach.
Published April 20, 2005.
Math Subject Classifications: 49M15, 46T25, 47H25.
Key Words: Newton method; star-like functions; continuous semigroup.
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| Yakov Lutsky |
Department of Mathematics
Ort Braude College
Karmiel 21982, Israel
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