Question

In MATLAB write a function secant.m to apply the secant method.

function [x,i] = secant(f, x0, x1, tol, maxiters) [x,i] = secant(f, x0, x1, tol, maxiters)

performs the secant method with f(x), starting at x_0 = x0 and x_1 = x1, and continuing until either |x_i+1 - x_i| <= tol, or maxiters iterations have been taken.

The number of iterations, i, is also returned. An error is raised if the first input is not a function handle. A warning is raised if the maximum number of iterations is reached without achieving the tolerance.

Test the function on the problem f(x) = 0.9 cos(x) - sqrt(x) = 0, with starting values x0 = 0 and x1 - 1, and a tolerance of 10^-8 and maxiters of 20.

Do not use previous answer on Chegg as it's not working

Thank you!

Answer 1

MATLAB code for the problem is provided below, please comment if any doubts related to program running or other quires related to this answer:

MATLAB code:

%Test code to define the function
%%function definition is at the end
%assign the given function
f = @(x)( 0.9*cos(x) - sqrt(x))

%set the inital values given in the question
x0 = 0;
x1 = 1;

%set the tolerance value
tol = 10^-8;

%set maximum iters value
maxiters = 20;

%execute the method using above values
[x, i] =secant(f,x0,x1,tol,maxiters)

%print the results
fprintf('The root, x = %f', x)
fprintf('f(x)= %f', f(x))

%%secant function definition

function [x,i] = secant(f,x0,x1,tol,maxiters)

   %find the first assumption
root = (x0*f(x1) - x1*f(x0))/(f(x1) - f(x0));

%set the iteration count as 0
iterationCount = 0;

%the infinte while loop to repeat till
%root gets with in the tolerance or
%exceed the maximum iteration number
while (1)
x0 = x1;
x1 = root;
  
%%Check if the tolerance limit reached
if(abs(x0 - x1 )< tol)
break;
end
  
       %find the next approximation
root = (x0*f(x1) - x1*f(x0))/(f(x1) - f(x0));

       %increase the iteration count
iterationCount = iterationCount + 1;
  
%%terminate if not toleration limit
   %reached with maximum iteration
   %with warning
if(iterationCount == maxiters)
disp('Warning!!!maximum iteration limit reached')
break;
end
end
  
   %assign the results
x=root;
i=iterationCount;
end

Output: