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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 \(f(z)-t_ if(z_ 0)=0\), \(0\leq t_ i\leq 1\), to solve \(f(z)=0\).

MSC:
65J15 Numerical solutions to equations with nonlinear operators
65H10 Numerical computation of solutions to systems of equations
47J25 Iterative procedures involving nonlinear operators