I need to find the smallest possible root.

I don't understand how to make this work.I need to find the smallest possible root and have an output/printout which needs to include the root x^*, the value f(x^*), the number of iterations performed and whether convergence was reached or the maximum number of iterations was reached before convergence was achieved. With the stopping criterion f(x^*)<10^(-5), maximum iterations set to 20 and start with xL=0 and xR=2.5. This what I have, but it won't run, also I don't know how to do printout.

clear all;
xL=0
xR=2.5
for j=1:20
xM=(xL+xR)/2;
fM=sin(3*xM)-2cos(xM);
fL=sin(3*xL)-2cos(xL);
fR=sin(3*xR)-2cos(xR);
if fM*fL<0
  xR=xM
elseif fM*fR<0
  xL=xM
  end
  if abs(fM)<10^(-5)
    break
    end
    end

Answer 1

[Walter Roberson]

fM=sin(3*xM)-2cos(xM);

MATLAB does not support implicit multiplication. You need a "*" or ".*" between the "2" and the "cos"

[Ewynne]

Yeah, I finally figured that out. But now I cant figure out how to get the number of iterations to print and how to tell if it converged before the 20th iteration and how to get that to also print. This is what I have....

clear all;
xL=0
xR=2.5 
for j=1:20
  xM=(xL+xR)/2;
  fM=sin(3*xM)-2*cos(xM);
  fL=sin(3*xL)-2*cos(xL);
  fR=sin(3*xR)-2*cos(xR);
  if fM*fL<0
    xR=xM
  else
    xL=xM
    end
    if abs(fM)<10^(-5)
      break
    end
end
xM
fM

[Ewynne]

Also, thank you!

[Walter Roberson]

xL=0
xR=2.5 
root_found = false;
for j=1:20
  fprintf('Iteration #%d\n', j);
  xM=(xL+xR)/2;
  fM=sin(3*xM)-2*cos(xM);
  fL=sin(3*xL)-2*cos(xL);
  fR=sin(3*xR)-2*cos(xR);
  if fM*fL<0
    xR=xM
  else
    xL=xM
    end
    if abs(fM)<10^(-5)
      root_found = true;
      break
    end
end
xM
fM