4. (30pts, 25, 5) Below is a MATLAB implementation of the bisection method with

Question

4. (30pts, 25, 5) Below is a MATLAB implementation of the bisection method with some code missing.

(a) Fill the blanks below to correctly execute the bisection method. READ CAREFULLY THE CODE !

function [c,err,n] = bisection(f,a,b,tol,N)

% function to solve f(x) = 0 using the bisection method over [a,b]

% ASSUMPTIONS: we assume that f(a)*f(b)<0

% INPUTS:

% f is the function at hand

% a is the lower bound of the tested interval

% b is the upper bound of the tested interval

% tol is the error tolerance

% N is the maximum number of iterations

% OUTPUTS:

% c is the computed root

% err is the error bound at the end

% n is the last iteration before breaking

n = 0;

a_n = a;

b_n = b;

err = b_n-a_n;

while err > tol && n < N

x_n = _____________;

if f(x_n)*f(a_n) > 0

______ = ______;

______ = ______;

elseif f(x_n)*f(b_n) >= 0

______ = ______;

______ = ______;

end

err = _____________;

n = n+1;

end

c = (b_n + a_n) / 2.0;

end

Explanation / Answer

Solution

Please find the below blanks from the question

(a) while err > tol && n < N

x_n = _(a_n+b_n)/2;___

if f(x_n)*f(a_n) > 0

a_n= x_n;

b_n = b_n;

elseif f(x_n)*f(b_n) >= 0

b_n = x_n;

a_n = a_n;

end

err = abs(f(a_n+b_n)/2);

n = n+1;

end

c = (b_n + a_n) / 2.0;

end

(b) For sure it is not working as f(a)*f(b)=1*16=16>0 since f(a)*f(b) has to be less than zero for initial [a,b]

Thank you!

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