MATLAB: How to write the MatLab code for the bisection method if we use |p(i)−p(i−1)|<ξ as a stopping criteria

MATLABnumerical method

function [akar,langkah]=bagidua3(a,b,tol)
iffeval('fun',a)*feval('fun',b)>0
error('akarnyatidakterjamin')
end
langkah=0;
akar=[];
p=(a+b)/2;fp=feval('fun',p);
while abs(b-a)>tol;
langkah=langkah+1;
    p=(a+b)/2;
akar=[akar,p];
fa=feval('fun',a);
fp=feval('fun',p);
if sign(fa)*sign(fp)<0
        a=a;
        b=p;
else
        a=p;
        b=b;
end
end
function y=fun(x)
y=x.^3-4*(x.^2)+sin(x)+1;
I know its somewhat look like this. But how i change it?

Best Answer

So just remember the former value of p and compare the changes equivalently to measuring the distance between a and b:
...
p    = a;
oldp = inf;
while abs(b - a) > tol && abs(p - oldp) > xsi
  langkah = langkah+1;
  oldp    = p;
  p       = (a + b) / 2;
  akar    = [akar, p];
  fa      = fun(a);
  fp      = fun(p);
  if sign(fa) * sign(fp) < 0
    b = p;    % But not a=a !!!
  else
    a = p;    % But not b=b !!!
  end
end
Avoid confusing lines like a=a. fun(a) is nicer than feval('fun', a) and it allows to provide a function handle as input.
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