Determine the natural cubic B-spline for a function in a table form of:
$$x_i\|-1\|0\|1\|2 \\ y_i\|-3\|0\|1\|2$$
So I'm very new to cubic splines and am quite lost on what I should do. I know I should express every point as a function of form $a_ix^3+b_ix^2+c_ix+d_i$ and then solve a system of equations with all of them but how am I supposed to show a pair like $(-1, -3)$ in such a form? I mean: aren't there infinitely many ways of doing it?
Any guidance on how to advance would be welcome :)