Matlab - RegulaFalsi

function [ X ] = RegulaFalsi( f,xai,xbi,tol )

syms x;

f1=subs(f,x,xai);

f2=subs(f,x,xbi);

i=1;

ea(1)=100;

if f1*f2 < 0

    xa(1)=xai;f1=subs(f,x,xa(1));

    xb(1)=xbi;f2=subs(f,x,xb(1));

    xr(1)=xa(1)-f1*(xb(1)-xa(1))/(f2-f1); f3=subs(f,x,xr(1));

    fprintf('It.              Xa           Xr            Xb            Error aprox \n');

    fprintf('%2d \t %11.7f \t %11.7f \t %11.7f \n',i,xa(i),xr(i),xb(i));

    while abs(ea(i))>=tol,

      if f1*f3 < 0

         xa(i+1)=xa(i);f1=subs(f,x,xa(i+1));

         xb(i+1)=xr(i);f2=subs(f,x,xb(i+1));

      end

      if f1*f3> 0

         xa(1)=xr(i);

         xb(1)=xb(i);

      end

      xr(i+1)=xa(i+1)-f1*(xb(i+1)-xa(i+1))/(f2-f1);

      ea(i+1)=abs((xr(i+1)-xr(i))/(xr(i+1)))*100;

      fprintf('%2d \t %11.7f \t %11.7f \t %11.7f \t %7.3f \n',...

              i+1,xa(i+1),xr(i+1),xb(i+1),ea(i+1));

      i=i+1;

   end

else

   fprintf('No existe una raíz en ese intervalo');

end

end

syms x;

f = x^2 -sin(x) -0.5;

% funcion f | intervalo [0,2] | tolerancia 10^-3 | error = 10^-3 | n = 4 

RegulaFalsi(f,0,2,10^-3)

% funcion f | intervalo [-1,0] | tolerancia 10^-3 | error = 10^-3 | n = 4 

RegulaFalsi(f,-1,0,10^-3)

% funcion f | intervalo [-1,0] | tolerancia 10^-3 | error = 10^-3 | n = 4 

RegulaFalsi(f,-1,0,10^-5)

function  X  = RegulaFalsi( f,xai,xbi,tol )

 syms x;

 f1=subs(f,x,xai);

f2=subs(f,x,xbi);

i=1;

ea(1,1)=100;

if f1*f2 < 0

    xa(1,1)=xai;   f1=subs(f,x,xa(1,1));

    xb(1,1)=xbi;   f2=subs(f,x,xb(1,1));

    xr(1,1)=xb(1,1)-f2*(xb(1,1)-xa(1,1))/(f2-f1); f3=subs(f,x,xr(1,1));

    fprintf('It.           Xa           Xr            Xb            Error aprox \n');

    fprintf('%2d    \t %11.7f   \t %11.7f \t %11.7f \n',i,double(xa(i,1)),double(xr(i,1)),double(xb(i,1)));

    while abs(ea(i,1))>=tol,

      if f1*f3 < 0

         xa(i+1,1)=xa(i,1);f1=subs(f,x,xa(i+1,1));

         xb(i+1,1)=xr(i,1);f2=subs(f,x,xb(i+1,1));

      end

         if f1*f3> 0

         xa(i+1,1)=xr(i,1);

         xb(i+1,1)=xb(i,1);

         end

      xr(i+1,1)=xb(i+1,1)-f2*(xb(i+1,1)-xa(i+1,1))/(f2-f1);

       f3=subs(f,x,xr(i+1,1));

      ea(i+1,1)=abs((xr(i+1,1)-xr(i,1))/(xr(i+1,1)))*100;

      fprintf('%2d \t %11.7f \t %11.7f \t %11.7f \t %7.3f \n',...

              i+1,double(xa(i+1,1)),double(xr(i+1,1)),double(xb(i+1,1)),double(ea(i+1,1)));

      i=i+1;

   end

else

   fprintf('No existe una raíz en ese intervalo');

end

end

>> syms x; f = x^2 -sin(x) -0.5;RegulaFalsi(f,0,2,10^-3)

It.           Xa           Xr            Xb            Error aprox

 1    	   0.0000000   	   0.3235510 	   2.0000000

 2 	   0.3235510 	   0.5947594 	   2.0000000 	  45.600

 3 	   0.5947594 	   0.8220929 	   2.0000000 	  27.653

 4 	   0.8220929 	   1.0126495 	   2.0000000 	  18.818

 5 	   1.0126495 	   1.1723786 	   2.0000000 	  13.624

 6 	   1.1723786 	   1.3062675 	   2.0000000 	  10.250

 7 	   1.1723786 	   1.1942989 	   1.3062675 	   9.375

 8 	   1.1942989 	   1.2126305 	   1.3062675 	   1.512

 9 	   1.1942989 	   1.1960609 	   1.2126305 	   1.385

10 	   1.1960609 	   1.1976535 	   1.2126305 	   0.133

11 	   1.1960609 	   1.1960820 	   1.1976535 	   0.131

12 	   1.1960820 	   1.1961028 	   1.1976535 	   0.002

13 	   1.1960820 	   1.1960820 	   1.1961028 	   0.002

14 	   1.1960820 	   1.1960821 	   1.1961028 	   0.000

>> fzero('x^2-sin(x)-0.5',1)

ans =

    1.1961