I am trying to store the values of each iteration of 0.01 in my for loop into a matrix. Could anyone help?

function [r k] = root_finder(f,x0,kmax,tol)
x1 = x0; %initial x1
        %for loop for x1 from 2 to kmax as intial value x1 is given
for i = 2 : kmax
%evaluating function f @x1 and comparing with tolerance given
if tol > abs(feval(f,x1))
r = x1; % if |f(xk)| < tol then we have to stop
k = i;
break;
else
x1 = x1 + 0.01; %incrementing x1 with 0.01
end
end
 
end %function ends

[J. Alex Lee]

You want to save the history of x1? It would only make sense if you wanted to also save the histories of the function value f (which you are trying to zero).

Typically, you would use "r" to denote the residual, or function value, so

function [rList,xList,k] = root_finder(f,x1,kmax,tol)

for k = 1 : kmax
    xList(i) = x1;
    % evaluating function f @x1 and comparing with tolerance given
    rList(i) = feval(f,x1);
    if tol > abs(r(i))
	break;
    end
    x1 = x1 + 0.01; %incrementing x1 with 0.01
end

end %function ends

Note that this is an objectively bad root-finding algorithm.

Also note that if your function f accepts vector x, then you could also do

xList = (x0:0.01:xEnd)
rList = f(xList)

[rBest,idxBest] = min(abs(rList))
xBest = xList(idxBest)

Answer 1

[Ayush Gupta]

The history of tolerance and corresponding x values can be stored if we treat them as vectors and in each iteration of for loop the value at that point is stored. Refer to the following code to see how it works:

function [r, k] = root_finder(f,x0,kmax,tol)
x1 = x0; %initial x1
        %for loop for x1 from 2 to kmax as intial value x1 is given
for i = 2 : kmax
%evaluating function f @x1 and comparing with tolerance given
    r(i) = abs(feval(f,x1));
    k(i) = x1;
    % if |f(xk)| < tol then we have to stop
    if tol >r(i)
       break;
    end
x1 = x1 + 0.01; %incrementing x1 with 0.01
end
 
end %function ends