📄 onepoint.mht

📁 it is a very essential matlab code.

💻 MHT

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<BODY><PRE>% Demonstration of One Point Iteration
clear; figure(1);clf;figure(2);clf;figure(1)

f =3D 'exp(-x)-x';       %define the function f(x)=3D0
g =3D 'exp(-x)';         %and a    x =3D g(x)   form

disp(['f(x) is ' f]);=20
disp(['g(x) is ' g]);

% plot the function
xmax=3D3;
grange =3D [-xmax xmax];
figure(1); ezplot(f,grange); hold on; line (grange, [0 0]); pause

% have a look at the g(x) function
figure(2); ezplot(g,[-1 xmax]);=20
hold on
plot([-1 xmax], [-1 xmax],'g')  % line defines x =3D x


x =3D input ('Enter initial guess of root:        ');
if length(x)=3D=3D0;x=3D0;end
maxerror =3D 0.1; % maximum error
   maxit =3D 30;  % maximum number of iterations
   count =3D 0;   % iteration counter
   error =3D 1;   % starting error (100 percent)

fprintf('\n Iteration      x       g(x)     error(%%)    f(x)\n\n');


% this is where all the work gets done.....
while (error &gt; maxerror) &amp; (count &lt; maxit)
  count =3D count + 1;
  xnew =3D eval(g);
  error =3D abs((xnew - x)/xnew) * 100;
  fprintf('%7g %10.4f %10.4f %10.4f  =
%10.4f\n',count,x,xnew,error,eval(f));
 =20
  %these 2 lines are added just to show the convergence graphically
  if count&gt;1;line([x x],[x xnew]);else;plot(x,eval(g),'r*');end
  line([x xnew],[xnew xnew]);pause
 =20
  x =3D xnew;
end

if count&lt;maxit
   fprintf('\nRoot is %g   Function at root is %g\n',x,eval(f))
   figure(1);plot(x,eval(f),'ro')
   figure(2);plot(x,eval(g),'ro')       % circle at root found
end


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