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arXiv · 2601.04708

On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases

Congpei An·Alvise Sommariva·Marco Vianello
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Abstract

We compute numerically the $L^2$ Marcinkiewicz-Zygmund constants of cubature rules, with a special attention to their role in polynomial approximation by orthogonal bases. We test some relevant rules on domains such as the interval, the square, the disk, the triangle, the cube and the sphere. The approximation power of the corresponding least squares (LS) projection is compared with standard hyperinterpolation and its recently proposed ``exactness-relaxed'' version. The Matlab codes used for these tests are available in open-source form.

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Congpei An, Alvise Sommariva, Marco Vianello. 2026-01-08. On the role of weak Marcinkiewicz-Zygmund constants in polynomial approximation by orthogonal bases. https://arxiv.org/abs/2601.04708

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