Let's suppose that we want to calculate a linear regression solution $X$ of data $Y$ via the design matrix $M$.
The solution to such a problem is known as:
$$X=M^{+}Y$$
Where $M$ results from evaluating the regression model over the discrete domain $D$ of the data $Y$. For a fixed domain $D$ it is possible to pre-calculate the pseudoinverse
$$M^{+}$$
What if the data $Y$ would be sparse over $D$, i.e. only few data points were existing/available over a few points of the domain $D$. Could it be of any help to know the pre calculated pseudoinverse
$$M^{+}$$
of the full domain $D$?