Question

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Answer 1

%% MATLAB code begins %%

% Test values
a_test = 0.25;
x0_test = 0;
eps_test = [15, 5, 2, 1];

% Testing
for a = a_test
    for eps = eps_test
        for x0 = x0_test
            fprintf("For a = %f, eps = %f%%, x0 = %f, mysqrt(a) = %f\n", a, eps, x0, mysqrt(a, eps, x0));
        end
    end
end

% Function
function [sqrta, n] = mysqrt(a, epsilon, x0)
    if nargin == 2      % If only 2 args,
        x0 = 0;         % set x0 to default value
    end
    n = 0;              % number of iterations
    sqrta = x0;         % initial value
    epsilon = epsilon / 100 * sqrt(a);      % Doing this will simplify the while condition
    while(abs(sqrt(a) - sqrta) > epsilon)   % While error is unacceptable
        sqrta = sqrta^2 + a;        % Recurrence relation
        n = n + 1;                  % One iteration done
    end
end

%% MATLAB code ends %%