Edit the Regula Falsi code to use a functional stopping criteria that will stop the code when either the process reaches the maximum iterations or when∣f(xn)∣<ftol for a specified tolerance ftol replacing the current error tolerance. Make the code useftol=1×10−4by default if that argument slot is left empty. Include the adapted code using the lab's naming scheme, and provide a comparison of the two stopping criteria for discussion in the pdf report. Are there any pros or cons? Is there any scenarios where one stopping criteria might be better or worse than the other?

Code:

function [r, k] = RegulaFalsi(f, a, b, kmax, tol)

%

% RegulaFalsi uses the regula falsi method to approximate a root of f(x) = 0

% in the interval [a,b].

%

% [r, k] = RegulaFalsi(f, a, b, kmax, tol), where

%

% f is an anonymous function representing f(x),

% a and b are the limits of interval [a,b],

% kmax is the maximum number of iterations (default 20),

% tol is the scalar tolerance for convergence (default 1e-4),

%

% r is the approximate root of f(x) = 0,

% k is the number of iterations needed for convergence.

%

if nargin < 5 || isempty(tol), tol = 1e-4; end

if nargin < 4 || isempty(kmax), kmax = 20; end

c = zeros(1,kmax); % Pre-allocate

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

r = 'failure';

return

end

disp(' k a b')

for k = 1:kmax,

c(k) = (a*f(b)-b*f(a))/(f(b)-f(a)); % Find the x-intercept

if f(c(k)) == 0 % Stop if a root has been found

return

end

fprintf('%2i %11.6f%11.6f',k,a,b)

if f(b)*f(c(k)) > 0 % Check sign changes

b = c(k); % Adjust the endpoint of interval

else a = c(k);

end

c(k+1) = (a*f(b)-b*f(a))/(f(b)-f(a)); % Find the next x-intercept

if abs(c(k+1)-c(k)) < tol, % Stop if tolerance is met

r = c(k+1);

return

end

end