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Newton’s method estimates from data at one point. (English) Zbl 0613.65058
The merging of disciplines: new directions in pure, applied, and computational mathematics, Proc. Symp. Honor G. S. Young, Laramie/Wyo. 1985, 185-196 (1986).

[For the entire collection see Zbl 0598.00007.]

The results in this paper are important for our construction of global algorithms based on Newton’s method, and for estimation of the efficiency of those algorithms. The idea is simply to apply the theorems here to a finite sequence of equations of the form f(z)-t i f(z 0 )=0, 0t i 1, to solve f(z)=0.


MSC:
65J15Equations with nonlinear operators (numerical methods)
65H10Systems of nonlinear equations (numerical methods)
47J25Iterative procedures (nonlinear operator equations)