Consider a 4-point natural spline. I want to use the spline for interpolation between two points $y_1,y_2$, when having access to four equidistant points (w.r.t $x$ axis).
Is the solution for the coefficients the following, as given here?
$a_0 = y_3 - y_2 - y_0 + y_1$
$a_1 = y_0 - y_1 - a_0$
$a_2 = y_2 - y_0$
$a_3 = y_1$
If not, what is the type of this cubic interpolation?
EDIT: The coefficients do not match natural spline. However, the interpolation also does not go through each point.
EDIT 2: The solution comes from first derivatives, setting $f'(0)=a_2=y_2-y_0$ and $f'(1)=a_0+a_1+a_2+a_3=y_3-y_1$.