The double descent and Runge phenomena in overparametrized polynomial interpolation

The paper investigates overparameterized polynomial interpolation across three polynomial bases—Monomial, Chebyshev, and Legendre—using coefficients minimal in the σ^2-norm (and σ^1-norm for the monomial basis). It focuses on equidistant and Chebyshev data points, though many findings hold regardless of sampling specifics. The study draws parallels between the classical Runge phenomenon and the modern double descent phenomenon in machine learning.

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