Modify the given Matlab code for the bisection algorithm so that the outputs are

Q: Modify the given Matlab code for the bisection algorithm so that the outputs are

function [root,iter,res] = bisection(fx,a,b,tol) % Method of bisection. if nargin tol*2 mid = (a+b)/2; fmid = fx(mid); if fa*fmid

ID: 3888844 • Letter: M

Question

Modify the given Matlab code for the bisection algorithm so that the outputs are n, an, bn, pn=(an+bn)/2, f(pn) and bn-an. Stop the alorithm when abs(bn-an)<10-12 or after 45 iterations, whichever comes first.

function [root,iter,res] = bisection(fx,a,b,tol)

% Method of bisection.

if nargin < 4, tol = eps;

end

fa = fx(a); fb = fx(b); iter = 0;

while abs(a-b) > tol*max(abs(a),abs(b))

mid = (a+b)/2; fmid = fx(mid);

if fa*fmid<=0

% There is a root in [a,mid].

b = mid; fb = fmid;

else

% There is a root in [mid,b].

a = mid; fa = fmid;

end

iter = iter + 1;

end

root = (a+b)/2;

res = fx(root);

So I'm assuming we can set tol=10-12 but I don't know how to check when I need to stop. I also am not sure how to modify the outputs/ inputs and how that would look. Any help greatly appreciated.

Explanation / Answer

function [root,iter,res] = bisection(fx,a,b,tol)

% Method of bisection.

if nargin < 4

tol = eps;

end

fa = fx(a); fb = fx(b); iter = 0;

while abs(a-b) > tol*2