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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Newest papers, page 7
Learning PDE solution operators with variable initial conditions via Latent Dynamics Networks
In many-query scenarios, data-driven surrogate models provide an efficient alternative to high-fidelity solvers for simulating physical systems governed by Partial Differential Equations (PDEs).Large Growth Happens: Gaussian Elimination with Partial Pivoting on Random Matrices
We prove that the probability that Gaussian elimination with partial pivoting on $n \times n$ random matrices has growth $ρ$ is at least inverse quasi-polynomial: $Ω(\exp(-c \log^2 (ρ)\log(n)))$ for…Inferring physical fields in coupled systems with unknown parameters from incomplete observations using physics-constrained attentive neural operators
Given incomplete measurements of a single physical field in a coupled system with unknown parameters, can we infer its full physical state and identify the underlying parameters?Global error estimators for parametric monotone nonlinearities and neural approximations
We construct computable error estimators, which double as loss functions for neural networks, for a class of parametric nonlinear partial differential equations with a monotonicity property, and…On the Sequentially Semiseparable Structure of SDE-Induced Kernels and Efficient Algorithms for Kernel-Based Estimation Problems
We study kernel functions induced by a linear time-invariant (LTI) stochastic differential equation (SDE), an approach that embeds prior knowledge about the function to be estimated directly into…Near-Exact Computation of Independent Chip Model Placement Probabilities for Thousands of Players
The Independent Chip Model (ICM) converts the chip stacks of the players remaining in a poker tournament into finishing-place probabilities and prize equities.Sharp dimensional analysis of midpoint methods for Langevin sampling
We study deterministic and randomized midpoint discretizations of Langevin dynamics for a target $π\propto e^{-V}$, where $0 \prec αI\preceq\nabla^2V\preceqβI$ and $κ=β/α$.IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs
Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accurate and typically…Singular parameters and missing limits in neural PDE solvers
Neural solvers for partial differential equations (PDEs) can approach an accurate solution while their parameters grow without bound.An overview of machine learning-enhanced iterative methods for systems of linear and nonlinear equations
Systems of equations arise in a wide range of scientific and engineering applications.Ground state energy estimation and preparation by the truncated power method
The Guided Local Hamiltonian Problem (GLHP) is the problem of ground state energy estimation and preparation given a guiding state having good overlap with the true ground state.Nontrivial periodic solutions to the one-phase free boundary problem
We construct new classical global solutions of the one-phase Bernoulli free boundary problem in $\mathbb{R}^3$ whose positive phases are periodic perturbations of the product of the…Checkable NTK Positivity and Finite-Width Gradient Descent for Scalar- and Vector-Valued PINNs with Strong-Form, Weak-Form, and Nonlocal Linear Constraints
We give checkable positive-definiteness criteria for the limiting neural tangent kernel (NTK) and high-probability finite-width gradient-descent guarantees for scalar- or vector-valued…CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations
Despite the growing popularity of physics-informed neural networks (PINNs), their applicability in the long-time integration of partial differential equations (PDEs) remains constrained.The Numerical Linear Algebra of Large Language Models
Numerical Linear Algebra (NLA) has consistently played a vital role in advancing science by providing tools to solve fundamental problems encountered in scientific and engineering applications.Sharp Riesz capacity inequalities and the Pólya--Szegő conjecture
For $n\geq2$ and $p\in(n-2,n)$, we prove that closed balls maximize the ratio of Riesz $p$-capacity to Newtonian capacity among all compact subsets of $\mathbb{R}^n$.A hybrid CNN-adjoint optimization framework for reconstruction of viscoelastic tissue properties in magnetic resonance elastography
Magnetic resonance elastography (MRE) is a noninvasive imaging modality for quantifying the viscoelastic properties of soft tissues from shear wave propagation.Latent Score-Based Bayesian Cramér-Rao Bound Estimation for High-Dimensional Imaging Systems
We propose a data-driven framework for estimating the Bayesian Cramér-Rao bound (CRB) in high-dimensional imaging systems with complex, analytically intractable priors.On architectural choices for interpretability and thermodynamic consistency in Physically Recurrent Neural Networks in the low-data regime
In this paper, we unravel the effect of different decoder architectures on the interpretability of the latent space of the Physically Recurrent Neural Network.On the Pricing of American Options under Stochastic Local Volatility and Stochastic Correlation via the RBSDE Framework
In this work, we study the pricing of American options under stochastic local volatility (SLV) models extended by including stochastic correlation driven by an additional stochastic process.