File:Quadratic interpolation.svg
Summary
| Description |
English: example of quadratic interpolation |
| Date | |
| Source | Own work |
| Author | User:DaBler |
Licensing
 |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
Source code
Plotted in GNU Octave:
clear;
figure(1);
subplot(211);
hold off;
x = [-1 0 1];
y = [-1 3 2];
stem( x, y );
hold on;
a = (y(1)-2*y(2)+y(3))/2;
b = (y(3)-y(1))/2;
c = y(2);
t = [-2000:+2000]./1000;
p = a*t.*t+b*t+c;
plot( t, p );
t_max = -b/2/a;
p_max = a*t_max.*t_max+b*t_max+c;
h=stem( t_max, p_max, "r" );
ylim([-2 5]);
xlim([-2 2])
legend("f[x]", "f(x)", "f(x) = max")
xlabel("x");
ylabel("y","Rotation",0);
subplot(212);
hold off;
plot( t(1:end-1), diff(p,1) );
hold on;
h=stem(t_max, 0, "r");
xlim([-2 2])
legend("f'(x)", "f'(x) = 0")
xlabel("x");
ylabel("y","Rotation",0);
print("quadratic_interpolation.svg");