Método de Newton-Raphson

X	f(x)		Ecuación	=	x^2-x-2		X1	f(X1)	f'(X1)	X0	e%	Respuesta
-10	108		Ecuación derivada	=	2x-1		0	-2	-1	-2	100
-9	88		X1	=	0		-2	4	-5	-1.2	66.6666667
-8	70		e%	=	0.01		-1.2	0.64	-3.4	-1.01176471	18.6046512
-7	54						-1.01176471	0.035432526	-3.02352941	-1.00004578	1.17183924
-6	40						-1.00004578	0.000137333	-3.00009155	-1	0.00457764	-1
-5	28						-1	2.09548E-09	-3	-1	6.9849E-08	-1
-4	18						-1	0	-3	-1	0	-1
-3	10						-1	0	-3	-1	0	-1
-2	4						-1	0	-3	-1	0	-1
-1	0						-1	0	-3	-1	0	-1
0	-2						-1	0	-3	-1	0	-1
1	-2						-1	0	-3	-1	0	-1
2	0						-1	0	-3	-1	0	-1
3	4						-1	0	-3	-1	0	-1
4	10						-1	0	-3	-1	0	-1
5	18
6	28
7	40
8	54
9	70
10	88

matlab

function x = Newt_n(f_name, xO)

% Iteración de Newton sin gráficos

x = xO; xb = x-999;

n=0; del_x = 0.01;

while abs(x-xb)>0.000001

  n=n+1; xb=x ;

  if n>300 break; end

  y=feval(f_name, x) ;

  y_driv=(feval(f_name, x+del_x) - y)/del_x;

  x = xb - y/y_driv ;

  fprintf(' n=%3.0f, x=%12.5e, y=%12.5e, ', n,x,y)

  fprintf(' yd = %12.5e \n', y_driv)

end

fprintf('\n Respuesta final = %12.6e\n', x) ;

f(x) = (x – 3) (x – 1) (x – 1)

n	xn	f(xn)	f'(xn)	xn+1
0	0.50000000	-0.62500000	2.75000000	0.72727273
1	0.72727273	-0.16904583	1.31404959	0.85591767
2	0.85591767	-0.04451055	0.63860849	0.92561694
3	0.92561694	-0.01147723	0.31413077	0.96215341
4	0.96215341	-0.00291894	0.15568346	0.98090260
5	0.98090260	-0.00073639	0.07748373	0.99040636
6	0.99040636	-0.00018496	0.03865069	0.99519176
7	0.99519176	-0.00004635	0.01930234	0.99759300
8	0.99759300	-0.00001160	0.00964539	0.99879578
9	0.99879578	-0.00000290	0.00482125	0.99939771
10	0.99939771	-0.00000073	0.00241026	0.99969881