PreprintarXiv licencearXiv
The double descent and Runge phenomena in overparametrized polynomial interpolation
Abstract
The Runge phenomenon in polynomial interpolation is often considered a classical analogue of the double descent phenomenon in machine learning. In this note, we explore overparameterized polynomial interpolation in three popular polynomial bases: Monomial, Chebyshev and Legendre basis with coefficients that are minimal in the ℓ2-norm (and, for the monomial basis, also those minimal in the ℓ1-norm). We present our results primarily for equidistant and Chebyshev data points, but many results are independent of the exact form of sampling.
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BibTeX
@misc{wein2026double,
title = {{The double descent and Runge phenomena in overparametrized polynomial interpolation}},
author = {Jason Wein and Stephan Wojtowytsch},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37657},
eprint = {2609.37657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37657},
}
RIS
TY - UNPB
TI - The double descent and Runge phenomena in overparametrized polynomial interpolation
AU - Jason Wein
AU - Stephan Wojtowytsch
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37657
UR - https://arxiv.org/abs/2609.37657
AB - The Runge phenomenon in polynomial interpolation is often considered a classical analogue of the double descent phenomenon in machine learning. In this note, we explore overparameterized polynomial interpolation in three popular polynomial bases: Monomial, Chebyshev and Legendre basis with coefficients that are minimal in the ℓ^2-norm (and, for the monomial basis, also those minimal in the ℓ^1-norm). We present our results primarily for equidistant and Chebyshev data points, but many results are independent of the exact form of sampling.
ER -