newton_iteration.m

function res=newton_iteration(x_value_list,fx)
% \param x_value_list: list of start position
% \param fx: syms expression
% \return res: the root value of fx
%
% can change precision and max_iteration_times and min_diff_value at the following
precision=1e-6;
max_iteration_times=20;
min_diff_value=1e-4;
% ------------------------------------------------------------%
% example:
% syms x;
% fx=x^2-2*x*exp(-x)+exp(-2*x);
% newton_iteration([0.5 0.6 0.7],fx);
%
% return
% the answer is
%     0.5671
%     0.5672
%     0.5672
% ------------------------------------------------------------%

syms x;
diff_fx=diff(fx);
fx_next=x-fx/diff_fx;
res=zeros(1,size(x_value_list,2));
for i = 1:size(x_value_list,2)
    first_x_value=x_value_list(i);
    x_before=double(first_x_value);
    x_next=double(subs(fx_next,x,x_before));
    
    iterate_times=1;
    while (abs(x_next-x_before)>precision) && (iterate_times<=max_iteration_times)
        % if f'x < min_diff_value,
        % return
        if abs(subs(diff_fx,x,x_before))<min_diff_value
            fprintf('\n diff less than min_diff_value \n min diff value is %06f\n', ...
                double(abs(subs(diff_fx,x,x_before))));
            break;
        end
        
        % print each iterate x_next value
        fprintf('\nthe current x_value is %f,\nthe current iterate_times is %d\n', ...
            x_next,iterate_times);
        
        % next iterate
        x_before=x_next;
        x_next=double(subs(fx_next,x,x_before));
        iterate_times=iterate_times+1;
    end
    res(i)=x_next;
end
fprintf('\nthe answer is\n');
fprintf('\n%f\n',res);
end