Showing papers by "Vlastimil Pták published in 1975"

The rate of convergence of Newton's process

Abstract: The author applies the method of nondiscrete mathematical induction (see [2---5]) which involves considering the rate of convergence as a function, not as a number, to Newton's process and proves that the rate of convergence is $$\omega (r) = \frac{{r^2 }}{{2(r^2 + d)^{1/2} }}$$ whered is a positive number depending on the initial data (see Theorem 2.3).