use bairstow’s method and matlab to determine the roots of (a) f(x) = −2 + 6.2x − 4x2 + 0.7x3 in matlab

main.m
function [roots] = bairstow_method(a, epsilon)
    n = length(a) - 1;  % degree of the polynomial

    % Initialize arrays to store the coefficients
    b = zeros(1, n);
    c = zeros(1, n);

    % Initialize the variables
    error = 1;
    max_iters = 100;
    iter = 0;

    while n > 2 && error > epsilon && iter < max_iters
        iter = iter + 1;

        % Initialize the guess values
        u = complex(rand(), rand());
        v = complex(rand(), rand());

        % Initialize the error terms
        du = complex(0, 0);
        dv = complex(0, 0);

        % Perform the Bairstow's iteration
        while true
            b(n) = a(n) - c(n + 1) * u - c(n + 2) * v;
            for i = n - 1:-1:1
                b(i) = a(i) - b(i + 1) * u - b(i + 2) * v;
            end

            c(n) = b(n) - du * u - dv * v;
            for i = n - 1:-1:1
                c(i) = b(i) - c(i + 1) * u - c(i + 2) * v;
            end

            det = c(2) * c(2) - c(1) * c(3);
            if det == 0
                % Break out of the loop if division by zero
                break;
            end

            % Update the guesses
            du = (b(1) * c(3) - b(2) * c(2)) / det;
            dv = (b(2) * c(1) - b(1) * c(2)) / det;

            % Update the coefficients
            u = u + du;
            v = v + dv;

            % Calculate the error
            error = abs(du) + abs(dv);

            % Break out of the loop if the error is within the desired accuracy
            if error < epsilon
                break;
            end
        end

        % Update the coefficients for the next step
        a = b(3:end);
        n = n - 2;
    end

    % Obtain the remaining roots using quadratic equation
    if n == 2
        roots = roots([a(2) a(1) 1]);
    else
        roots = roots([a(1) 1]);
    end
end
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main.m
% Define the polynomial coefficients
a = [0.7 -4 6.2 -2];

% Set the desired accuracy
epsilon = 1e-6;

% Find the roots using Bairstow's method
roots = bairstow_method(a, epsilon);

% Display the roots
disp("The roots are:");
disp(roots);
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