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A fixed point proof of the convergence of a Newton-type method. (English) Zbl 1115.65053
The convergence of the Newton iteration and the convergence of a Newton-like iteration for a nonlinear scalar equation is discussed. Because there exists a close connection between Newton type iterative methods and fixed point theory, the authors apply a fixed point approach in theirs investigations. The convergence results are obtained under weaker smoothness conditions on the function from the left hand side of the equation and its first derivative. The error estimate derived for the Newton-like method is better than the estimate obtained for the classical Newton method .
MSC:
65H05 Numerical computation of solutions to single equations
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