math.NA · 2026-07-29 · No. 68

Numerical Analysis, 2026-07-29.

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

    Massively parallel numerical simulations with Julia

    Simon Candelaresi, Benedict Geihe, Marco Artiano, Lars Christmann, Valentin Churavy, Andrés Rueda-Ramírez, Hendrik...

    math.NA · cs.DC · cs.MS · cs.PF

    The Julia programming language aims to provide a modern approach to develop high-performance computing (HPC) applications. It tries to achieve this by combining a high-level, dynamic interface with just-in-time compilation to native machine code, thereby facilitating high developer productivity and native code performance at the same time. While this approach has already been shown to work well for serial applications, it is not clear if it...

    arxiv.org/abs/2607.25866 · PDF

  2. 02

    Automated Numerical Stability Analysis of Deep Learning Operators

    Xinye Chen

    math.NA · cs.AI

    Finite-precision arithmetic unavoidably introduces numerical approximation errors. Numerical computations may use insufficient precision or an improper formulation, which leads to numerical instability. In this paper, we introduce the first unified software tool that integrates CESTAC for detecting the numerical stability of deep learning operators. Our developed software not only enables numerical validation with a single computation pass...

    arxiv.org/abs/2607.25494 · 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.