Plotting a graphical converge inside a While - Newton Raphson numerical method

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Luis Francisco Sanchez 2019-8-26

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https://ww2.mathworks.cn/matlabcentral/answers/477539-plotting-a-graphical-converge-inside-a-while-newton-raphson-numerical-method

评论： David Wilson 2019-8-27

Hi, I'm trying to get a command inside a while so as the Newton Rapshon code shows a graphical converge. If the values of the aproximations are connected between a line, it shows something like a spider web. Can anyone help me out, please?

Here is my code:

clear 
clc
syms x
f = input('Introducir la función: '); %function
p0 = input ('Introducir valor semilla: '); %first aproximation
TOL = input ('Introducir la tolerancia de error: '); %error
fplot (f)
grid on
hold on
derivada = diff(f);
derivada = inline (derivada);
f = inline (f);
eabs = 100;
i =0;
while eabs>TOL
    p = p0 - (f(p0))/(derivada(p0));
    eabs = abs(((p-p0)/p)*100);
    p0 = p;
    i = i+1;
end
fprintf('\n Valor= %8.3f  ',p0)
plot (p)
fplot (0)
hold off

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Walter Roberson 2019-8-27

p = asin(sin(p));

David Wilson 2019-8-27

Another solution assuming you are looking for an iterative numerial stragegy that stays strictly within the given bounds is to use bisection. Sure it is slow, but it will stay within the -pi/2 to +pi/2 bound.

F = @(x)  -x +cos(x)+tan(x); % function of interest 
eps = 0.0; tol = 1e-6;  % assume some stopping tolerance, set eps to 0.1 if nervous
x = [-pi/2+eps, pi/2-eps]; 
Fx = F(x); % should be vectorised
assert(prod(sign(Fx)) < 0,'x does not bracket root')
while abs(diff(x)) > tol % Now start bisection routine 
  m = mean(x); % mid point, m = (a + b)/2
  fm = F(m); % find f(m)
  if Fx(1)*fm > 0
    x(1)=m; Fx(1)=fm; % discard left
  else
    x(2)=m; % discard right
  end % if
end % while