math.NA · 2026-07-31 · No. 70

Numerical Analysis, 2026-07-31.

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

    Graph Neural Multilevel Preconditioners for Iterative Solvers

    Zechen Zhang, Rui Peng Li, Yousef Saad

    math.NA · cs.LG

    Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning. While classical methods such as algebraic multigrid (AMG) are highly scalable, their robustness can degrade on indefinite or nonsymmetric systems where heuristics originally developed for elliptic PDEs are less reliable. Recently, Graph Neural Networks (GNNs) have emerged as...

    arxiv.org/abs/2607.28456 · PDF

  2. 02

    Windowed thinning and query complexity for the bouncy particle and Zigzag samplers

    Jianfeng Lu, Yinchen Luo

    math.NA · cs.LG · math.PR · math.ST

    Let $μ(d x)\propto e^{-U(x)} d x$ on $\R^d$, where $U$ is $m$-strongly convex and $L$-smooth, and denote by $κ=L/m$ the condition number. We consider windowed thinning, an exact simulation method for the bouncy particle sampler and the coordinate Zigzag process. The method divides a trajectory into deterministic windows and uses a gradient evaluation at the beginning of each window to construct a tractable local envelope for the event rate....

    arxiv.org/abs/2607.28413 · PDF

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