Hello we have to implement the bisection method to find a root of a function in the interval [a,b]. The algorithm should return 1.the root "c" 2. the function value "yc" 3. number of iterations "itcount".
Here is what I have till now:
function [ r, c, yc, itcount] = bisection( f, a, b, N, eps )
% Check that that neither end-point is a root
% and if f(a) and f(b) have the same sign, throw an exception.
if ( f(a) == 0 )
r = a;
return;
elseif ( f(b) == 0 )
r = b;
return;
elseif ( f(a) * f(b) > 0 )
error( 'f(a) and f(b) do not have opposite signs' );
end
% We will iterate N times and if a root was not
% found after N iterations, an exception will be thrown.
for k = 1:N
% Find the mid-point
c = (a + b)/2;
yc = feval(f,c);
itcount = abs(b-a)/2;
% Check if we found a root or whether or not
% we should continue with:
% [a, c] if f(a) and f(c) have opposite signs, or
% [c, b] if f(c) and f(b) have opposite signs.
if ( f(c) == 0 )
r = c;
return;
elseif ( f(c)*f(a) < 0 )
b = c;
else
a = c;
end
% If |b - a| < eps_step, check whether or not
% |f(a)| < |f(b)| and |f(a)| < eps_abs and return 'a', or
% |f(b)| < eps_abs and return 'b'.
if ( b - a < eps )
if ( abs( f(a) ) < abs( f(b) ) && abs( f(a) ) < eps )
r = a;
return;
elseif ( abs( f(b) ) < eps )
r = b;
return;
end
end
end
error( 'the method did not converge' );
end
I have already created a .m file for the function I want to find the root of. And the algorithm works but it only returns the root but not the function value and the number of iterations. What am I doing wrong?
