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The rate of convergence of Newton's process (1975)

Pták, Vlastimil

Springer

Numerische Mathematik 25 (1975), S. 279-285

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ISSN: 0945-3245

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary 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).

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01399416

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