Let $f:[k_1,k_n]\to\mathbb{R}$ be a degree $d$ B-spline function with real knots $\{k_1,\ \ldots\ ,\ k_n\}$ and real coefficients $\{c_1,\ \ldots\ ,c_{n-d-1}\}$.
The norm $\ \int_{k_1}^{k_n}f(t)^2dt\ \ $ is a quadratic form wrt. the coefficients.
I have been trying for some time to understand its matrix and how to conveniently compute it (e.g. using matrix multiplications and recursions). But even when considering just the case where all knots are distinct for simplicity, I fail to see how to this should be done.
The explicit expressions seems to be smaller when the basis functions are scaled to be a partition of unity rather than scaled by their integral, but I don't a priori have a preference to the scaling.
I have looked at the article 'Integrating Products of B-Splines', but it's only about the computing the value of the norm.
Any hints / related references are appreciated