生成时间: 2026年05月08日 05:20:37

重点关注论文数量: 0

了解领域论文数量: 2

不相关论文数量: 20

了解领域论文（摘要翻译）

1. 基于调和延拓的体-表面切割有限元法的稳定化与算子预处理

Stabilization and Operator Preconditioning of Bulk–Surface CutFEM via Harmonic Extension

作者: Qing Xia

类别: math.NA, physics.comp-ph

发布日期: 2026-05-07

arXiv ID: 2605.06329v1

链接: http://arxiv.org/abs/2605.06329v1

摘要翻译

中文标题: 基于调和延拓的体-表面切割有限元法的稳定化与算子预处理

摘要翻译: 我们提出一种用于光滑闭曲线$Γ\subset\mathbb{R}^2$上Laplace-Beltrami方程的切割有限元方法(CutFEM)，该方法与$Ω$中的调和体问题耦合，且\emph{无需显式稳定化}：无需鬼惩罚、法向梯度惩罚或单元聚合。切割单元上迹有限元空间的经典病态性源于在$Γ$上具有渐消小支集的基函数；我们的观察是，通过背景笛卡尔网格上的格点Green函数(LGF)实现将曲面离散与离散体调和延拓耦合，可严格约束导致该病态性的自由度。缩减算子由完整CutFEM刚度的合同变换得到，继承了变分形式的对称性和半正定性，并且其条件数在最小切割单元比下一致有界。直接重构具有标准的$O(h^{-2})$网格条件数；单层密度公式起到算子预处理的作用并产生$O(1)$条件数，这适用于迭代求解器；双层密度公式保持切割无关且具有$O(h^{-2})$的缩放。在标准正则性假设下，我们证明了$H^1(Γ)$/$L^2(Γ)$中的最优$O(h)$/$O(h^2)$误差估计，严格建立了切割无关的条件数，并通过数值实验展示了最优收敛速率和对小切割的鲁棒性。

2. 向量场乘子算子与矩阵值核拟插值

Vector field multiplier operators and matrix-valued kernel quasi-interpolation

作者: Zhengjie Sun, Biao Huang, Xingping Sun

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05610v1

链接: http://arxiv.org/abs/2605.05610v1

摘要翻译

中文标题: 向量场乘子算子与矩阵值核拟插值

摘要翻译: 我们建立并分析了一类矩阵值球面卷积核，这些核源自 $\mathbb{S}^2$（嵌入 $\mathbb{R}^3$ 中的单位球面）上经尺度变换的带函数。这些核的构造利用了 Legendre 微分方程，并对原始带核的正则性条件要求更弱。所诱导的积分算子是简单的 Fourier-Legendre 乘子，它们不仅（关于尺度参数）提供了最优的 Sobolev 误差估计，而且在 $\mathbb{S}^2$ 上的 $L_2$ 切向量场上产生了自然的 Helmholtz-Hodge 分解。通过对底层卷积积分进行离散化，我们获得一族向量值拟插值，它们在无散或无旋向量场中实现了我们的逼近目标。该拟插值算法对含噪数据具有鲁棒性。实现过程可适应人工调整，既不涉及计算卷积积分，也不需求解线性方程组。拟插值算法的计算效率和执行鲁棒性与现有基于核的向量场插值方法形成鲜明对比。

不相关论文（基本信息）

1. 基于FFT插值的无矩阵求逆极小问题求解

Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation

作者: Haidong Wu, Snehal Bhayani, Janne Heikkilä

类别: cs.CV, math.NA

发布日期: 2026-05-07

arXiv ID: 2605.06572v1

链接: http://arxiv.org/abs/2605.06572v1

摘要: Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Gröbner-basis or resultant-based methods due to matrix inversion needed in the online solver. Here we propose a sampling-based, matrix inversion-free method that constructs the solvers using sparse hidden-variable resultants. The determinant polynomial in the hidden variable is efficiently reconstructed via inverse fast Fourier transform interpolation from sampled evaluations, avoiding symbolic expansion. Solving this polynomial yields the hidden variable, and the remaining unknowns are recovered by identifying rank-1 deficient submatrices and applying Cramer’s rule. A greatest common divisor-based criterion ensures robust submatrix identification under noise. Experiments on diverse minimal problems demonstrate that the proposed solver achieves strong numerical stability and competitive runtime, particularly for small-scale problems, providing a practical alternative to traditional Gröbner-basis and resultant-based solvers.

2. 参数化粘塑性浅流的降阶建模

Reduced-Order Modeling of Parameterized Visco-Plastic Shallow Flows

作者: Md Rezwan Bin Mizan, Ilya Timofeyev, Maxim Olshanskii

类别: physics.flu-dyn, math.NA

发布日期: 2026-05-07

arXiv ID: 2605.06526v1

链接: http://arxiv.org/abs/2605.06526v1

摘要: We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel–Bulkley fluids. These flows exhibit strong nonlinearities, non-smooth rheology, moving fronts, and yield surfaces, making efficient surrogate modeling particularly challenging. To address this challenge, we employ a tensor-based approach in which the solution manifold is approximated using a low-rank representation obtained via higher-order singular value decomposition of snapshot data over a structured parameter space. The resulting tensorial reduced-order model (TROM) enables rapid online evaluation by directly reconstructing solution trajectories from the compressed representation, thereby avoiding the need to perform time integration of a reduced dynamical system. The proposed non-intrusive framework can be interpreted as an encoder–decoder architecture with a compressed latent representation and efficient multilinear decoding. Numerical experiments demonstrate that the proposed approach accurately captures key flow features, including front propagation, plug and shear regions, and near-stopping dynamics, while achieving substantial computational speedups relative to full-order simulations.

3. 辛Stiefel流形上具有闭式逆的极因子收缩

A polar-factor retraction on the symplectic Stiefel manifold with closed-form inverse

作者: Ralf Zimmermann

类别: math.NA, math-ph, math.DG

发布日期: 2026-05-07

arXiv ID: 2605.06399v1

链接: http://arxiv.org/abs/2605.06399v1

摘要: In Riemannian computing applications, it is crucial to map manifold data to a Euclidean domain, where vector space arithmetic is available, and back. Classical manifold theory guarantees the existence of such mappings, called charts and parameterizations, or, collectively, local coordinates. When computational efficiency is of the essence, practitioners usually resort to retraction maps to define local coordinates. Retractions yield first-order approximations of the Riemannian normal coordinates. This work introduces a new retraction on the symplectic Stiefel manifold that features a closed-form inverse. We expose essential features and compare the numerical performance to a selection of existing retractions. To the best of our knowledge, prior to this work, the so-called Cayley retraction was the only retraction on the symplectic Stiefel manifold with known closed-form inverse.

4. 低秩核方法在美式期权定价中的应用

Low-rank kernel methods for American option pricing

作者: Michael Multerer, Paul Schneider, Chiara Segala

类别: math.NA, math.ST

发布日期: 2026-05-07

arXiv ID: 2605.06349v1

链接: http://arxiv.org/abs/2605.06349v1

摘要: We propose a scalable and theoretically grounded low-rank conditional expectation model for recursive Monte Carlo optimal stopping problems, in particular American option pricing. Our method reformulates the estimation of continuation values as a learning problem in a reproducing kernel Hilbert space, in which the conditional expectation is represented as a linear operator acting on future payoffs. This perspective yields an offline-online decomposition: the operator is learned once from simulated data and subsequently reused across all exercise dates, eliminating the need to recompute regression models at each step of the backward recursion. We establish convergence guarantees and derive bounds quantifying the approximation errors across exercise dates. Numerical experiments demonstrate the speed and accuracy of the proposed approach relative to extant methods.

5. 非线性RMM-GKS用于具有不确定正演算子的大规模动态与流式逆问题

Nonlinear RMM-GKS for Large-Scale Dynamic and Streaming Inverse Problems with Uncertain Forward Operators

作者: Toluwani Okunola, Mirjeta Pasha, Misha E. Kilmer, James G. Nagy, Eric de Sturler

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.06336v1

链接: http://arxiv.org/abs/2605.06336v1

摘要: Many practical imaging systems suffer from uncertainty in acquisition geometry – such as projection angles in computed tomography or sensor positions in photoacoustic tomography – leading to nonlinear inverse problems that require joint estimation of both the image and the forward model parameters. Standard approaches that assume a known linear forward operator fail to account for these uncertainties, resulting in significant reconstruction artifacts. We propose a nonlinear recycled majorization-minimization generalized Krylov subspace (NL-RMM-GKS) framework for large-scale inverse problems with uncertain forward operators. The method extends MM-GKS to nonlinear settings by combining majorization-minimization for nonsmooth regularization with Krylov subspace projection and subspace recycling, ensuring bounded memory usage. Two complementary formulations are developed: an alternating minimization approach that alternates between image updates and Gauss-Newton parameter estimation, and a variable projection approach that eliminates the image variable and optimizes directly over the parameters using inexact inner solves. We further introduce streaming variants that process data sequentially, enabling reconstruction from large or dynamically acquired datasets without storing the full operator. For dynamic problems, we incorporate two temporal regularization strategies – optical flow and anisotropic total variation – as plug-in choices within the framework. We carry out rigorous numerical experiments in fan-beam computed tomography and photoacoustic tomography to demonstrate that our proposed framework achieves high-quality reconstructions with bounded memory requirements, making it suitable for large-scale dynamic imaging problems.

6. INEUS：高维偏积分微分方程的迭代神经求解器

INEUS: Iterative Neural Solver for High-Dimensional PIDEs

作者: Jean-Loup Dupret, Davide Gallon, Patrick Cheridito

类别: cs.LG, math.NA, q-fin.CP

发布日期: 2026-05-07

arXiv ID: 2605.06281v1

链接: http://arxiv.org/abs/2605.06281v1

摘要: In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal jump integrals with single-jump sampling and reformulates PIDE solving as a sequence of recursive regression problems. Like Physics-Informed Neural Networks (PINNs), INEUS learns global solutions over the entire space-time domain, yet it offers a more efficient treatment of nonlocal terms and avoids the computationally expensive differentiation of full PIDE residuals. These features make INEUS particularly well suited for high-dimensional PDEs and PIDEs. Supported by a contraction-based convergence proof for linear PIDEs, our numerical experiments show that INEUS delivers accurate and scalable solutions for various high-dimensional linear and nonlinear examples.

7. 双李普希茨归一化流的表达能力：基于分数扩散的视角

Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective

作者: Meira Iske, Carola-Bibiane Schönlieb

类别: stat.ML, cs.LG, math.NA, math.PR

发布日期: 2026-05-07

arXiv ID: 2605.06172v1

链接: http://arxiv.org/abs/2605.06172v1

摘要: Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based diffusion models. For the probability flow ODE of a variance-preserving diffusion, Lipschitz regularity of the score induces a flow of bi-Lipschitz diffeomorphic transport maps. This ODE bridge allows us to analyze the distributional approximation power of bi-Lipschitz normalizing flows and, conversely, derive deterministic convergence guarantees for diffusion-based transport. Our key idea is to use the probability flow ODE to link regularity of the score to regularity of the induced transport maps. We verify score regularity for broad target densities, including compactly supported densities, Gaussian convolutions of compactly supported measures and finite Gaussian mixtures. We obtain a universal distributional approximation result: Gaussian pullbacks induced by bi-Lipschitz variance-preserving transport maps are $L^1$-dense among all probability densities. For Gaussian convolution targets, we further obtain convergence in Kullback-Leibler divergence without early stopping.

8. Euler-Bernoulli梁的双边特征值界

Two-sided eigenvalue bounds for the Euler-Bernoulli beam

作者: Jana Burkotova, Jitka Machalova, Tomas Vejchodsky

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.06031v1

链接: http://arxiv.org/abs/2605.06031v1

摘要: We derive novel guaranteed lower bounds for eigenvalues of the Euler-Bernoulli beam with variable bending stiffness. While the standard finite element Rayleigh-Ritz method automatically yields upper bounds, we obtain lower bounds by employing interpolation error estimates with the explicitly known value of the associated constant. This approach is especially efficient and easy to apply for piecewise constant bending stiffness. For general variable material parameters, we obtain guaranteed lower bounds through an auxiliary beam-bending problem. The first eigenvalue is of primary interest in applications because it represents the critical load that causes buckling of the beam. Our method is, however, suitable also for the higher buckling modes. In addition, it can be applied to the physically more relevant nonlinear Gao beam model with piecewise constant bending stiffness, which has the same first eigenvalue as the classical Euler–Bernoulli beam. The presented numerical experiments illustrate the performance of the proposed eigenvalue bounds, demonstrating their convergence rates.

9. DBMSolver: 一种用于高质量图像到图像翻译的无训练扩散桥采样器

DBMSolver: A Training-free Diffusion Bridge Sampler for High-Quality Image-to-Image Translation

作者: Sankarshana Venugopal, Mohammad Mostafavi, Jonghyun Choi

类别: cs.CV, cs.AI, cs.LG, math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05889v1

链接: http://arxiv.org/abs/2605.05889v1

摘要: Diffusion-based image-to-image (I2I) translation excels in high-fidelity generation but suffers from slow sampling in state-of-the-art Diffusion Bridge Models (DBMs), often requiring dozens of function evaluations (NFEs). We introduce DBMSolver, a training-free sampler that exploits the semi-linear structure of DBM’s underlying SDE and ODE via exponential integrators, yielding highly-efficient 1st- and 2nd-order solutions. This reduces NFEs by up to 5x while boosting quality (e.g., FID drops 53% on DIODE at 20 NFEs vs. 2nd-order baseline). Experiments on inpainting, stylization, and semantics-to-image tasks across resolutions up to 256x256 show DBMSolver sets new SOTA efficiency-quality tradeoffs, enabling real-world applicability. Our code is publicly available at https://github.com/snumprlab/dbmsolver.

10. 针对双基地测量定制的双聚焦方法的数学与实验验证

Mathematical and experimental validation of the bifocusing method tailored for bistatic measurement

作者: Won-Kwang Park

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05845v1

链接: http://arxiv.org/abs/2605.05845v1

摘要: In this paper, we design a bifocusing-based imaging strategy for the rapid identification of small penetrable dielectric inhomogeneities within a two-dimensional bistatic measurement setup. To address the applicability and limitation, we carefully explore the mathematical structure of the indicator function by establishing a relationship involving the infinite series of Bessel functions, the material characteristics, and the bistatic angle. Through this theoretical result, we rigorously verify that the imaging resolution degrades as the bistatic angle approaches $\SI{180}{\degree}$, and specifically, that target identification becomes impossible when the bistatic angle is $\SI{180}{\degree}$. Conversely, relatively high-resolution results are obtained when the bistatic angle is close to $\SI{0}{\degree}$. The theoretical findings are validated through numerical simulations using the Fresnel experimental dataset, which confirm the applicability and limitations of the proposed method for both dielectric and metallic objects.

11. 通过函数型形状数据分析与拟共形映射的平面形态测量学

Planar morphometry via functional shape data analysis and quasi-conformal mappings

作者: Hangyu Li, Gary P. T. Choi

类别: q-bio.QM, cs.CG, math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05778v1

链接: http://arxiv.org/abs/2605.05778v1

摘要: The study of shapes is one of the most fundamental problems in life sciences. Although numerous methods have been developed for the morphometry of planar biological shapes over the past several decades, most of them focus solely on either the outer silhouettes or the interior features of the shapes without capturing the coupling between them. Moreover, many existing shape mapping techniques are limited to establishing correspondence between planar structures without further allowing for the quantitative analysis or modelling of shape changes. In this work, we introduce FDA-QC, a novel planar morphometry method that combines functional shape data analysis (FDA) techniques and quasi-conformal (QC) mappings, taking both the boundary and interior of the planar shapes into consideration. Specifically, closed planar curves are represented by their square-root velocity functions and registered by elastic matching in the function space. The induced boundary correspondence is then extended to the entire planar domains by a quasi-conformal map, optionally with landmark constraints. Moreover, the proposed FDA-QC method can naturally lead to a unified framework for shape morphing and shape variation quantification. We apply the FDA-QC method to various leaf and insect wing datasets, and the experimental results show that the proposed combined approach captures morphological variation more effectively than purely boundary-based or interior-based descriptions. Altogether, our work paves a new way for understanding the growth and form of planar biological shapes.

12. 正权核求积的凸几何误差界

Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature

作者: Satoshi Hayakawa

类别: math.NA, cs.LG, math.PR, stat.ML

发布日期: 2026-05-07

arXiv ID: 2605.05705v1

链接: http://arxiv.org/abs/2605.05705v1

摘要: Kernel quadrature can exploit RKHS spectral structure and outperform Monte Carlo on smooth integrands, but optimized quadrature weights are generally signed and may be numerically unstable. We study whether spectral acceleration remains possible when the weights are constrained to be positive, i.e., simplex weights. In the exact-target fixed-pool setting, an evaluated i.i.d. candidate pool of size $N$ is already available and the task is to reweight it so as to approximate the kernel mean embedding. We show that this positive reweighting problem is governed not by the equal-weight empirical average, but by the random convex hull generated by the pool. Our main geometric result shows that the mean of a bounded $d$-dimensional random vector can be approximated by a convex combination of $N$ i.i.d. samples at accuracy $O(d/N)$ with high probability, sharper than equal-weight averaging in the fixed-dimensional regime. We transfer this $d$-dimensional convex-hull approximation to full RKHS worst-case error through an augmented Mercer-truncation argument. The resulting positive-weight KQ bounds consist of a spectral tail term and a finite-sample convex-hull term, yielding Monte-Carlo-beating rates in favorable spectral regimes, including near-$O(1/N)$ rates up to logarithmic factors under exponential spectral decay. We also provide a constructive Frank–Wolfe algorithm that operates directly on the pool atoms, maintains simplex weights, and admits an explicit optimization-error bound.

13. 二维不可压缩流的隐式-显式Runge-Kutta方法的长时间稳定性

Long-time stability of implicit-explicit Runge-Kutta methods for two-dimensional incompressible flows

作者: Hong-lin Liao, Xiaoming Wang, Xuping Wang, Cao Wen

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05645v1

链接: http://arxiv.org/abs/2605.05645v1

摘要: High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dynamical behaviors. While several high-order implicit-explicit schemes have been proposed in the literature, their long-time stability properties remain largely unexplored. We develop a family of long-time stable implicit-explicit Runge-Kutta (IERK) methods, up to fourth-order temporal accuracy, for the two-dimensional incompressible Navier-Stokes equations in vorticity-stream function formulation. By combining a convolution-type Hölder inequality with a damping-type multistage Grönwall inequality, we establish a unified analytical framework that proves long-time stability in both the $L^2$ and $H^1$ norms. A key component of the analysis is a mathematical-induction argument that ensures stage-wise boundedness of the vorticity in the $H^δ$ norm for some $δ>0$. To the best of our knowledge, this is the first work to establish large-time stability results for high-order IERK algorithms for the two-dimensional incompressible Navier-Stokes equations. Our IERK schemes employ stiffly accurate diagonally implicit Runge-Kutta approximations for the linear diffusive term together with explicit Runge-Kutta approximations for the nonlinear advection term. By exploiting the specific structure of the Navier-Stokes model, we derive a reduced set of order conditions-requiring only 5 and 11 conditions for the third- and fourth-order methods, respectively, in contrast to the classical 6 and 18-allowing the construction of a parameterized family of efficient schemes. These IERK methods are particularly well suited for adaptive time-stepping, as they permit significantly enlarged step sizes in actual computations.

14. 加权 $L^2$ 投影的新误差估计

New error estimates of the weighted $L^2$ projections

作者: Qiya Hu, Yuhan Luo

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05637v1

链接: http://arxiv.org/abs/2605.05637v1

摘要: It is known that the weighted $L^2$ projection operator exhibits approximation properties different from those of the classical $L^2$ projection, in the sense that the $L^2$ error of the weighted $L^2$ projection of an $H^1$ function generally cannot be bounded by the $H^1$ semi-norm of the function. In this paper, we establish sharper $L^2$ error estimates for the weighted $L^2$ projection of an $H^1$ function under general weight distributions. These new estimates show that the $L^2$ errors of the weighted $L^2$ projection can be controlled by the $H^1$ semi-norm of the function, except when the weight distribution is highly irregular, such as those resembling a ``checkerboard" pattern. These results can be applied to more refined analyses of domain decomposition methods and multigrid methods for certain partial differential equations with large jump coefficients.

15. 非线性抛物方程隐-显多步方法稳定性的半生成函数方法

A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations

作者: Hong-lin Liao, Chaoyu Quan, Tao Tang, Tao Zhou

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05619v1

链接: http://arxiv.org/abs/2605.05619v1

摘要: The rigorous stability analysis of high-order implicit-explicit multistep (IEMS) methods for nonlinear parabolic equations by using discrete energy arguments is a long standing open issue due to their non-A-stable property. A novel semi-generating function approach combined with the global discrete energy analysis is suggested to the stability and convergence analysis of general IEMS methods for nonlinear parabolic equations. Inspired from the Grenander-Szegö theorem for the Toeplitz matrix, the semi-generating function approach is used to handle the three groups of discrete coefficients via three complex rational polynomials on the unit circle. A unified theoretical framework is then presented to establish the unconditional stability of IEMS methods if the minimum eigenvalue of composite convolution kernels for the implicit part is properly large and the spectral norm bound of composite convolution kernels for the explicit part is properly small. An indicator, called implicit-explicit controllability intensity, is then introduced to evaluate the degree of controllability of implicit part over explicit part. Some of existing IEMS methods, up to the fifth-order time accuracy, are revisited and compared by computing the associated implicit-explicit controllability intensities such that one can choose certain IEMS method or proper parameter to maintain the unconditional stability for a specific nonlinear parabolic model. We also propose a new parameterized class of IEMS methods, up to the eighth-order time accuracy, which satisfy the priori settings of our theory and have a large value of the implicit-explicit controllability intensity by choosing proper parameter so that they would be well suited for a wide class of nonlinear parabolic problems.

16. 次扩散方程中时空依赖源项识别的数值分析

Numerical Analysis of Space-Time Dependent Source Identification in Subdiffusion Equations

作者: Siyu Cen, Bangti Jin, Yavar Kian, Zhi Zhou

类别: math.NA, math.AP

发布日期: 2026-05-07

arXiv ID: 2605.05579v1

链接: http://arxiv.org/abs/2605.05579v1

摘要: In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method for spatial discretization with a finite difference method for temporal discretization. We establish the linear convergence of the fixed-point iteration and derive an error bound that depends explicitly on the discretization parameters and the noise level. The error analysis relies on stability properties of the continuous inverse problem and technical estimates for the associated direct problem with limited-regularity data. Numerical experiments are presented to support and complement the theoretical analysis.

17. 求解大型不定最小二乘问题的双分裂迭代法

The double splitting iteration method for solving the large indefinite least squares problem

作者: Jun Li, Lingsheng Meng

类别: math.NA

发布日期: 2026-05-07

arXiv ID: 2605.05551v1

链接: http://arxiv.org/abs/2605.05551v1

摘要: Addressing large-scale indefinite least squares (ILS) problem poses notable computational bottlenecks in the field of numerical linear algebra. State-of-the-art iterative schemes for such problems are predominantly constructed upon the single splitting of the coefficient matrix derived from the corresponding normal equation. In this work, we put forward an innovative iterative framework grounded in the double splitting of normal equations tailored for ILS problem. Specifically, we elaborate on a distinct implementations of the double splitting strategy, which offer constructive insights and methodological references for subsequent research on double splitting-based iterative methods. Two numerical experiments further corroborate that the proposed double splitting iterative paradigm outperforms conventional single splitting approaches in both computational efficiency and convergence robustness.

18. 用于多孔弹性波传播且具有对称应力近似的杂交间断伽辽金方法

Hybridizable discontinuous Galerkin methods for poroelastic wave propagation with symmetric stress approximation

作者: Jeonghun J. Lee, Manuel A. Sanchez

类别: math.NA

发布日期: 2026-05-06

arXiv ID: 2605.05451v1

链接: http://arxiv.org/abs/2605.05451v1

摘要: In this paper, we develop hybridized discontinuous Galerkin (HDG) methods for poroelastic wave equations. We first rewrite the governing equations to a first-order symmetric hyperbolic system in order to use dual mixed formulations for discretization. Subsequently, we combine two HDG approaches in the discretization of the system, the $\text{HDG}+$ method for the linear elasticity equations and the $\text{LDG-H}$ method for the diffusion equations, with adjustments for the poroelastic wave equations. In our proposed HDG methods, the numerical approximation of the stress tensor is strongly symmetric and the convergence of the errors are robust for nearly incompressible materials. Upon performing static condensation, the system retains numerical trace variables solely for the solid displacement and the fluid pressure. We provide comprehensive error analyses for both the semidiscrete formulation and the Crank–Nicolson time-stepping scheme. Finally, extensive numerical examples illustrate optimal convergence results and simulate different poroelastic wave propagation scenarios relevant in the literature.

19. 条件生成压缩感知的主动学习

Active Learning for Conditional Generative Compressed Sensing

作者: Alexander DeLise, Nick Dexter

类别: cs.LG, math.NA

发布日期: 2026-05-06

arXiv ID: 2605.05435v1

链接: http://arxiv.org/abs/2605.05435v1

摘要: Generative compressed sensing uses the range of a pretrained generator as a nonlinear model for recovering structured signals from limited measurements. We study a conditional version of this problem for image recovery from subsampled Fourier measurements using prompt-conditioned generative models. Our framework separates two roles of conditioning: the prompt used to design the sampling distribution and the prompt used to define the recovery model. For ReLU and Lipschitz conditional generators, we prove stable recovery bounds showing that prompt-matched Christoffel sampling retains the same Christoffel complexity constant as existing near-optimal generative compressed sensing theory, while prompt mismatch incurs an explicit compatibility penalty. Experiments with Stable Diffusion show that prompts meaningfully reshape Christoffel sampling distributions and influence image recovery. Overall, our results suggest that prompts should be treated as design variables with distinct effects on sensing, approximation, and recovery.

20. 借助广义高斯连分数映射生成高质量伪随机性

Producing Quality Pseudorandomness with a Generalized Gauss Continued-Fraction Map

作者: Benjamin V. Holt

类别: math.DS, math.NA

发布日期: 2026-05-06

arXiv ID: 2605.05378v1

链接: http://arxiv.org/abs/2605.05378v1

摘要: Well-known chaotic maps, such as the logistic and tent maps, have been used to generate cryptographically secure pseudorandomness, yet we know of no efforts which attempt to use the Gauss continued-fraction map, a known chaotic map, as a starting point for producing quality pseudorandom output. In this paper, we consider the family of $r$-continued-fraction maps, which generalize the Gauss map, and use them to generate pseudorandom output which outperforms many standard generators, such as the Mersenne Twister, in statistical quality, as ascertained by use of the Dieharder, PractRand, and TestU01 suites. In this way, we demonstrate the potential viability of these maps as a starting point for novel generators, and provide practical motivation for further study of the properties of both the exact and finite-precision $r$-continued fraction maps.