Numerical stability of the Halley-iteration for the solution of a system of nonlinear equations
Abstract: Let and a simple root in of the system of nonlinear equations .
Abstract Padé approximants (APA) and abstract Rational approximants (ARA) for the operator F have been introduced in  and . The adjective ``abstract'' refers to the use of abstract polynomials  for the construction of the rational operators.
The APA and ARA have been used for the solution of a system of nonlinear equations in . Of particular interest was the following third order iterative procedure:
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