EAS 502 Homework I

clear all;

function root = bisection(f, x0, x1, tol=1E-5)
                while (abs(x1 - x0)/2 > tol)
                                root = (x0 + x1) / 2; % calculate the new root.
                                if (f(x0) * f(root)) > 0
                                % if f(x0) and f(root) have same sign
                                                x0 = root;
                                else
                                                x1 = root;
                                end
                end
end

function x1 = newtons(f, f_dash, x0, tol=1E-5)
                err = 1;
                while (abs(err) > tol)
                                x1 = x0 - f(x0) / f_dash(x0);
                                err = x1 - x0;
                                x0 = x1;
                end
end

function x2 = chords(f, x0, x1, tol=1E-5)
                err = (x1 - x0);
                while (abs(err) > tol)
                                x2 = x0 - f(x0) * (x1 - x0) / (f(x1) - f(x0));
                                err = x2 - x1;
                                x0 = x1;
                                x1 = x2;
                end
end


function x2 = secant(f, x0, x1, tol=1E-5)
                err = (x1 - x0);
                while (abs(err) > tol)
                                x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0));
                                err = x2 - x1;
                                x0 = x1;
                                x1 = x2;
                end
end


function x2 = false_pos(f, x0, x1, tol=1E-5)
                err = (x1 - x0);
                while (abs(err) > tol)
                                x2 = (f(x0) * x1 - f(x1) * x0) / (f(x0) - f(x1));
                                err = x2 - x1;
                                x0 = x1;
                                x1 = x2;
                end
end



% find_root (test subroutine)
function root = find_root(f, f_dash, x0, x1, method, tol=1E-5)
                if method == 'b'
                                root = bisection(f, x0, x1, tol);
                elseif method == 'n'
                                root = newtons(f, f_dash, x0, tol);
                elseif method == 's'
                                root = secant(f, x0, x1, tol);
                elseif method == 'c'
                                root = chords(f, x0, x1, tol);
                elseif method == 'f'
                                root = false_pos(f, x0, x1, tol);
                end
end


f = @(x) x.^3 - 20;
f_dash = @(x) 3.*x.^2;

x0 = 1;
x1 = 3;

find_root(f, f_dash, x0, x1, 'n') % newtons method.
find_root(f, f_dash, x0, x1, 'b') % bisection method.