**Abstract:** We discuss the relationship between the norm of the
local discrete least squares polynomial approximation operator, the minimal
singular value $\sigmam(P_\Xi)$ of the matrix $P_\Xi$ of the evaluations
of the basis polynomials, and the norming constant of the set of data points
$\Xi$ with respect to the space of polynomials. Since these three quantities
are equivalent up to bounded constants, and since $\sigmam(P_\Xi)$ can
be efficiently computed, it is feasible to use $\sigmam(P_\Xi)$ as a tool
for distinguishing good local point constellations, which is useful for
scattered data fitting. In addition, we give a simple new proof of a bound
by Reimer for the norm of the interpolation operators on the sphere and
extend it to discrete least squares operators.

**Preprint version available:** pdf

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