8 Implement a MATLAB function bisection.m of the form function [r, h] = bisectio

Question

8 Implement a MATLAB function bisection.m of the form function [r, h] = bisection(a, b, f, p, t) % a: Beginning of interval [a, b] %b: End of interval [a, b] % f: function handle y = f(x, p) % p: parameters to pass through to f % t: User-provided tolerance for interval width At each step J = 1 to n, carefully choose m as in geometric mlean bisection (watch out for zeroes!). Replace a, b] by the smallest interval with endpoints chosen from a, m, b whiclh keeps the root bracketed. Repeat until a f value exactly vanishes, b-a

Explanation / Answer

error('Wrong number of input arguments.');

elseif(nargin==3)

if(f(a)*f(b) >= 0)

disp(' The function has positive value at the end points of interval .');

disp('The root can't be found using bisection method, use some other method.');

root = 'Root can't be found using bisection method' ;

return;

else

fprintf('Iteration a b m f(a) f(b) f(m) ');

fprintf('============== ====== === ======= =========== );

m=(a+b)/2;

if (abs(f(m)) <= 1e-6)

root =m;

return;

else

Iter = 0;

while (abs(f(m) ) >= 1e -6)

Iter = Iter+1;

m = (a+b)/2;

if (f(a) *f(m) >0)

a =m ;

else

b = m;

end

fprintf(' % 3d' ,Iter);

fprintf(' %20.4f' ,a);

fprintf(' %12.4f' ,b);

fprintf(' %12.4f' ,m);

fprintf(' %14.4f' ,f(a);

fprintf(' % 16.4f' ,f(b));

fprintf(' % 16.4f' ,f(m));

fprintf(' ');

end

root = m;

end

end

end

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