Spline interpolation operator
= Spline interpolation operator
{title2=$P_{\mathbf x}f=\sum_j(A^{-1}Rf)_jN_j$}
For a fixed spline space and admissible interpolation sites, this linear operator sends a <continuous function> to its unique interpolating spline. Here $Rf$ is the vector of sampled values and $A$ is the <B-spline collocation matrix>. It reproduces every spline in its range. Its sensitivity to perturbing the data is quantified by the <B-spline interpolation operator norm>.