math.NA · 2026-09-06 · No. 107

Numerical Analysis, 2026-09-06.

2 new papers in math.NA. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    Residual neural networks overcome the curse of dimensionality for semilinear heat equations

    Ilkhom Mukhammadiev, Diyora Salimova

    math.NA · cs.LG · math.AP · math.PR

    Rigorous results show that feedforward neural networks can overcome the curse of dimensionality in the numerical approximation of high-dimensional partial differential equations (PDEs), but comparatively little is known about residual neural networks (ResNets) in the nonlinear PDE setting. We prove that ResNets overcome the curse of dimensionality in the numerical approximation of solutions of semilinear heat equations with globally Lipschitz...

    arxiv.org/abs/2609.03626 · PDF

  2. 02

    Spectral Convergence of Random Feature Method in Multiple Dimensions

    Pingbing Ming, Hao Yu

    math.NA · cs.AI · cs.LG · math.ST

    We first prove spectral convergence of the random feature method (RFM) for multidimensional targets in Sobolev, Gevrey, ultra-analytic, and bandlimited classes. The analysis establishes general high-probability approximation estimates in the interpolation scale generated by a kernel integral operator. On a single event determined only by the sampled features, one random space approximates every target in a prescribed source ball; moreover,...

    arxiv.org/abs/2609.03401 · PDF

This edition is part of The Daily Abstract — math.NA archive. Subscribe to receive these in your inbox each morning, automatically translated to Spanish, with reply-to-PDF: arxivdaily.ignorelist.com.

Colophon Set in Georgia, with system sans for interface chrome and a monospaced stack for code and paper identifiers. Sole accent: amber #D99C5E. Built and served on an always-free VM. The masthead is set 14% letterspaced because newspapers do that and it works.