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.

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