Plotting the tangent line for newton raphson method

How can I plot the tangent lines for the newton raphson method?

I tried it this way... (have a closer look at line 33 - 38)

% Nullstellen von 
%
%  y(x)  = x^2 - 2
%

clear, clc 

fx   = @(x) x.^2 -2
dfdx = @(x) 2*x

n_step = 7   ;  % Anzahl der durchzuführenden Schritte für Newtonverfahren

x0   = 5   ;  % Startwert

%%%% newton-verfahren %%%%%%%%%%%%

x    = zeros(n_step+1,1) ;
x(1) = x0                ; 

for i=1:n_step
    x(i+1) =  -   fx(x(i)) / dfdx(x(i))  + x(i)  ;
end

y = fx(x) ;  % zugehörige y-werte / Daten zum Plotten

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xx  = [1 : .01 : 5] ; % Daten zum plotten blaue Linie
yy  = fx(xx) ; % Daten zum plotten blaue Linie

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for j=1:3
    yt(j+1) = dfdx(x(j)) * (x(j)-x(j))+fx(x(j))


    xt(j+1) = -fx(x(j))/dfdx(x(j)) +x(j)
end


figure(1), clf

subplot(2,1,1), grid on, hold on
plot(xx,yy)
plot(x,y,'r--*')
title('Newton-Raphson-Verfahren')
legend('y=x^2-2','Newton-Verfahren','location','northwest')

subplot(2,1,2), grid on, hold on 
plot(xx,yy)
plot(x,y,'r*')
plot(xt,yt,'r.-')
title('Newton-Raphson-Verfahren')
legend('y=x^2-2','Newton-Verfahren','Tangenten','location','northwest')


%%%%% bildschirmausgabe *****************

format long

disp('************ Newton-Verfahren ***************')
disp('           x                y=f(x)  ')
disp([ x y ])

format short

The tangents should be generated in the secon for slope. (line 33 - 38)

After that, i want to plot it in the second subplot.

exception:

Thanks for helping me.

Answer 1

[Alan Stevens]

Like this?

fx   = @(x) x.^2 -2;
dfdx = @(x) 2*x;

n_step = 7   ;  % Anzahl der durchzuführenden Schritte für Newtonverfahren

x0   = 5   ;  % Startwert

%%%% newton-verfahren %%%%%%%%%%%%

x    = zeros(n_step+1,1) ;
x(1) = x0;
for i=1:n_step
    x(i+1) =  -   fx(x(i)) / dfdx(x(i))  + x(i)  ; 
end

y = fx(x) ;  % zugehörige y-werte / Daten zum Plotten

% Tangent line calcuations
xt = zeros(2*n_step+1,1); 
yt = zeros(2*n_step+1,1);
xt(1) = x(1); yt(1) = y(1);
for i = 1:n_step
   xt(2*i) = x(i+1);
   xt(2*i+1) = x(i+1);
   yt(2*i) = 0;
   yt(2*i+1) = fx(x(i+1));
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xx  = 1 : .01 : 5 ; % Daten zum plotten blaue Linie
yy  = fx(xx) ; % Daten zum plotten blaue Linie

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(1), clf

subplot(2,1,1), grid on, hold on
plot(xx,yy)
plot(x,y,'r--*')
title('Newton-Raphson-Verfahren')
legend('y=x^2-2','Newton-Verfahren','location','northwest')

subplot(2,1,2), grid on, hold on 
plot(xx,yy)
plot(x,y,'r*')
plot(xt,yt,'r.-')
title('Newton-Raphson-Verfahren')
legend('y=x^2-2','Newton-Verfahren','Tangenten','location','northwest')

%%%%% bildschirmausgabe *****************

format long

disp('************ Newton-Verfahren ***************')

************ Newton-Verfahren ***************

disp('           x                y=f(x)  ')

           x                y=f(x)  

disp([ x y ])

   5.000000000000000  23.000000000000000
   2.700000000000000   5.290000000000001
   1.720370370370370   0.959674211248285
   1.441455368177650   0.077793578448165
   1.414470981367771   0.000728157131505
   1.414213585796884   0.000000066252480
   1.414213562373095   0.000000000000000
   1.414213562373095  -0.000000000000000

format short

[Patrick Ofenloch]

perfect,

thank you!