MATLAB: What’s the difference

MATLABpiecewise interpolation

I want to piecewise plot a interlolation function. When I input the nodes like this 
X = -1:0.1:1;
N = length(X);
the graph is continuous like this
However When I input the nodes like this :
X = zeros(1,21);
N = 21;
for i = 1: 21
X(i) = -1 + 2*(i-1)/(N-1);
there is an obvious gap in the graph like this :
I suppose these two codes are exactly the same, why the graphs are different??
the codes are as follows:
tic
clc
clear
f = @(x)1./(1+25.*x.^2);
syms x 
f_dri = diff(f(x));
%X = -1:0.1:1;
%N = length(X);
 X = zeros(1,21);
 N = 21;
    F = zeros(1, N);
    F_dri = zeros(1, N);
    for i = 1 : N
       X(i) = -1 + 2*(i-1)/(N-1);
        F(i) = f(X(i));
        F_dri(i) = subs(f_dri, x, X(i));
    end
    for j = 1 : N-1
        M = zeros(4,4);
        M(1,1) = F(j);
        M(2,1) = F(j);
        M(3,1) = F(j+1);
        M(4,1) = F(j+1);
        M(2,2) = F_dri(j);
        M(3,2) = (F(j+1)-F(j))/(X(j+1)-X(j));
        M(4,2) = F_dri(j+1);
        M(3,3) = (M(3,2)-M(2,2))/(X(j+1)-X(j));
        M(4,3) = (M(4,2)-M(3,2))/(X(j+1)-X(j));
        M(4,4) = (M(4,3)-M(3,3))/(X(j+1)-X(j));
    f_inp = M(1,1)+(x-X(j))*M(2,2)+(x-X(j))^2*M(3,3)+(x-X(j+1))*(x-X(j))^2*M(4,4);
    a = X(j):0.01:X(j+1);
    b = subs(f_inp, x, a);
    G = plot(a, b, 'r', 'LineWidth', 2);
    hold on 
    end
     saveas(gcf, 'pic_2', 'jpg'); 
% r = -1:0.01:1;
% f_ori = f(r);
% G(5) = plot(r, f_ori, 'k', 'LineWidth', 2);
legend(G,'N=21');
toc

Best Answer

X(13) is eps/4 less than 0.2 . When you use X(j):0.01:X(j+1) that is just enough that the previous plot ends at 0.19 instead of 0.20
Always remember that when you calculate your endpoints using floating point numbers that they will usually not be **exactly* nice multiples of 1/10 or 1/100 .
Related Question