Improved error analysis of Newton's method for a certain class of operators
Keywords:
Nonlinear operator equation, Newton's method, Banach space, semilocal convergence, Smale's α-theory, Fréchet-derivative.Abstract
We present an improved error analysis for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation using Newton's method. The advantages of our approach under the same computational cost - as in earlier studies such as [15, 16, 17, 18, 19, 20] - are: weaker sufficient convergence condition; more precise error estimates on the distances involved and an at least as precise information on the location of the solution. These advantages are obtained by introducing the notion of the center γ0condition. A numerical example is also provided to compare the proposed error analysis to the older convergence analysis which shows that our analysis gives more precise error bounds than the earlier analysis.
Mathematics Subject Classification (2010): 47H17, 49M15.
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