This is the same Newton-Raphson method formula series as derived previously using the geometric method

Derivation of Newton Raphson method from Taylor series

Table 4. Oscillations near local maxima and minima in Newton Raphson method.

Iteration Number		f(xi)
9	-1.0000 0.5 -1.75 -0.30357 3.1423 1.2529 -0.17166 5.7395 2.6955 0.9770	3.00 2.25 5.062 2.092 11.874 3.57 2.029 34.942 9.268 2.954	_____ 300.00 128.571 476.47 109.66 150.80 829.88 102.99 112.927 175.96

Figure 6: Oscillations around local minima for

Newton-Raphson method can also be derived from Taylor series. For a general function f(x), the Taylor series is

+

As an approximation, taking only the first two terms of the right hand side,

and we are seeking a point where , that is, if we assume

which gives

NONLINEAR EQUATIONS
Topic	Newton-Raphson Method of Solving Nonlinear Equations
Summary	Text book notes of Newton Raphson method of finding roots of nonlinear equation, including convergence and pitfalls.
Major	General Engineering
Authors	Autar Kaw
Date	December 26, 2014
Web Site	http://numericalmethods.eng.usf.edu

Дата добавления: 2014-12-27