Applied Math · Mathematics & Statistics
Numerical Analysis
The newest papers in Numerical Analysis that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
285 papers, from 31 August 2026 to 5 November 2026: 212 arXiv preprints and 73 OpenAlex records.
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NEXT: Physics-Informed Neuro-Spectral Exponential Time Differencing Architectures
Physics-Informed Neural Networks (PINNs) build neural representations of time-dependent PDE solutions, naturally incorporating physics knowledge and observational data, which makes them well suited…Tight Convergence Bounds for the Classical Kaczmarz Method
The classical method of Kaczmarz, introduced in 1937, is a textbook iterative method for solving linear systems $A x = b.$ Despite its widespread use, particularly in the context of solving inverse…Distance-Residual Physics-Informed Neural Networks: A Deep Learning Framework for Differential and Partial Differential Inclusions
We introduce Distance-Residual Physics-Informed Neural Networks (DR-PINNs), a physics-informed learning framework for approximating solutions of ordinary and partial differential inclusions (DIs)…Singularity models for the Bernoulli free boundary problem from isoparametric hypersurfaces
We develop a general construction of homogeneous solutions to the Bernoulli free boundary problem, as well as general extremal domains on the sphere, from isoparametric foliations of the sphere.Elucidating the Conformal Structure of the Brinkman Penalisation Method for Geometry-Adapted, Structure-Preserving Operator Learning of Hamiltonian PDEs
The Brinkman penalisation method embeds boundary-value problems on complex domains into a simple computational box by modeling the solid region as a strongly dissipative medium, avoiding body-fitted…Convergence guarantees for Muon: New parameter regimes and generalizations
In this paper, we establish the first asymptotic convergence guarantees for the Muon algorithm through a more accurate proxy for the Newton-Schultz iteration than the typical matrix sign function.Stable solutions of the Allen--Cahn equation in dimension three are one-dimensional
We prove that every bounded stable solution of the Allen--Cahn equation in $\mathbb R^3$ is one-dimensional.KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators
Topology optimization (TO) remains computationally intensive due to repeated finite element analysis (FEA) evaluations required at each iteration.Sparse-Observation Atmospheric Thermal Forecasting with Physics-Informed Neural Networks for Climate-Aware Digital Twins
Short-horizon forecasts of atmospheric temperature are needed to support climate-aware digital-twin systems, but such forecasts must be produced where thermal observations are incomplete.A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problems
In this work, we propose a hybrid iterative deep Ritz method (H-IDRM) for a class of interface problems for second-order elliptic operators.Riemannian Structure and Optimization for a Class of Low-Parametric Orthogonal Matrices
In this paper, we are concerned with matrices formed by block-diagonal factors interleaved with fixed permutations -- a flexible family of structured matrices.Tensor Decomposition of Transformer Key-Value Caches: Spectral Structure and Format Comparison
The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and grouped layers.Hutch#: Optimal non-adaptive Frobenius norm estimation
The Girard--Hutchinson estimator provides an extremely simple randomized estimate of the Frobenius norm of a matrix $A$ that can only be accessed implicitly via matrix-vector products.Global Convergence of Third-Order Langevin Dynamics for Non-Convex Optimization via Simulated Annealing
We study global convergence guarantees of third-order Langevin dynamics for non-convex optimization via simulated annealing with fixed friction and decreasing noise.Eigenvalue and Eigenvector Approximation for Random Matrices Using Low-Degree Polynomials
We initiate the study of approximating the top eigenvalue and eigenvector of a random symmetric matrix $ A \in \mathbb{R}^{n\times n} $ using $ q(A)b $ where $q$ is a degree-$d$ polynomial and $b$…Spectral geometry: old questions and new answers
These are extended notes based on a series of lectures given by the author at the Institut de Mathematiques de Toulouse in June 2025.AURA: Angular Update Rate Adaptation for training complex-valued neural networks
Complex-valued neural networks (CVNNs) are increasingly adopted for complex-valued data; however, they are often trained with first-order optimizers inherited from the real-valued case.SuperPCA: subspace analysis and an efficient algorithm for high-dimensional PCA
Principal component analysis (PCA) is a fundamental tool to reduce the dimensionality of the data in many applications.One-Step Generative Surrogate Models via Block-Triangular Joint Drifting
Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned on the same current…Notes on Fourier-Bessel wavelets
These notes develop the mathematical foundations and construction of a Fourier-Bessel wavelet family inspired by the disk harmonics of Shaqfa et al.[9].