SIAM Journal on Numerical Analysis最新文献_第4页

Coarse Scrambling for Sobol’ and Niederreiter Sequences Sobol '和niederiter序列的粗置乱

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-15 DOI: 10.1137/25m1807514

Kosuke Suzuki

引用次数: 0

Pointwise-in-Time Error Bounds for Semilinear and Quasilinear Fractional Subdiffusion Equations on Graded Meshes 分级网格上半线性和拟线性分数次扩散方程的点向误差界

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-15 DOI: 10.1137/25m1769260

Seán Kelly, Natalia Kopteva

引用次数: 0

Global Convergence of Adaptive Least-Squares Finite Element Methods for Nonlinear PDEs 非线性偏微分方程自适应最小二乘有限元方法的全局收敛性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-14 DOI: 10.1137/25m1796746

Philipp Bringmann, Dirk Praetorius

{"title":"Global Convergence of Adaptive Least-Squares Finite Element Methods for Nonlinear PDEs","authors":"Philipp Bringmann, Dirk Praetorius","doi":"10.1137/25m1796746","DOIUrl":"https://doi.org/10.1137/25m1796746","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1239-1274, August 2026. <br/> Abstract. The Zarantonello fixed-point iteration is an established linearization scheme for quasi-linear PDEs with strongly monotone and Lipschitz continuous nonlinearity in Hilbert spaces. This paper presents a weighted least-squares minimization for the computation of the update of this scheme. The resulting formulation allows for a conforming least-squares finite element discretization of the primal and dual variables of the PDE with arbitrary polynomial degree. The least-squares functional provides a built-in a posteriori discretization error estimator in each linearization step motivating an adaptive Uzawa-type algorithm with an outer linearization loop and an inner adaptive mesh-refinement loop. For quasi-linear PDEs in divergence form satisfying a 2-growth condition, we prove global R-linear convergence of the computed linearization iterates for arbitrary initial guesses. Particular focus is on the role of the weights in the least-squares functional of the linearized problem and their influence on the robustness of the Zarantonello damping parameter. Numerical experiments illustrate the performance of the proposed algorithm.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"22 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148440914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Krylov and Core Transformation Algorithms for an Inverse Eigenvalue Problem to Compute Recurrences of Multiple Orthogonal Polynomials 计算多个正交多项式递归的特征值反问题的Krylov和Core变换算法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-09 DOI: 10.1137/25m1770965

Amin Faghih, Michele Rinelli, Marc Van Barel, Raf Vandebril, Robbe Vermeiren

引用次数: 0

A New Sparsity Promoting Residual Transform Operator for Lasso Regression Lasso回归的一种新的稀疏性提升残差变换算子

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-09 DOI: 10.1137/25m1772113

Yao Xiao, Anne Gelb, Aditya Viswanathan

{"title":"A New Sparsity Promoting Residual Transform Operator for Lasso Regression","authors":"Yao Xiao, Anne Gelb, Aditya Viswanathan","doi":"10.1137/25m1772113","DOIUrl":"https://doi.org/10.1137/25m1772113","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1217-1238, August 2026. <br/> Abstract. Lasso regression is a widely employed approach within the [math] regularization framework used to promote sparsity and recover piecewise smooth signals [math] when the given observations are obtained from noisy, blurred, and/or incomplete data environments. In choosing the regularizing sparsity-promoting operator, it is assumed that the particular type of variability of the underlying signal, for example, piecewise constant or piecewise linear behavior across the entire domain, is both known and fixed. Such an assumption is problematic in more general cases, e.g., when a signal exhibits piecewise oscillatory behavior with varying wavelengths and magnitudes. To address the limitations of assuming a fixed (and typically low order) variability when choosing a sparsity-promoting operator, this investigation proposes a novel residual transform operator that can be used within the Lasso regression formulation. In a nutshell, the idea is that for a general piecewise smooth signal [math], it is possible to design two operators [math] and [math] such that [math], where [math] is a discretized approximation of [math], but [math]. The corresponding residual transform operator, [math], yields a result that (1) effectively reduces the variability dependent error that occurs when applying either [math] or [math] to [math], a property that holds even when [math] is not a good approximation to the true sparse domain vector of [math], and (2) does not require [math] or [math] to have prior information regarding the variability of the underlying signal. Numerical experiments demonstrate the effectiveness of the new residual transform operator when compared to standard sparsity-promoting operators used in Lasso regression for recovering piecewise smooth signals.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"79 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148408826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Finite Difference Schemes for Hamilton–Jacobi Equation on the Wasserstein Space on Graphs 图上Wasserstein空间上Hamilton-Jacobi方程的有限差分格式

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-01 DOI: 10.1137/25m1754704

Jianbo Cui, Tonghe Dang, Chenchen Mou

{"title":"Finite Difference Schemes for Hamilton–Jacobi Equation on the Wasserstein Space on Graphs","authors":"Jianbo Cui, Tonghe Dang, Chenchen Mou","doi":"10.1137/25m1754704","DOIUrl":"https://doi.org/10.1137/25m1754704","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1126-1161, August 2026. <br/> Abstract. This work proposes and studies numerical schemes for initial value problems of Hamilton–Jacobi equations (HJEs) with a graph individual noise on the Wasserstein space on graphs. Numerically solving such equations is particularly challenging due to the structural complexity caused by discrete geometric derivatives and logarithmic geometry. Our numerical schemes are constructed using finite difference approximations that are adapted to both the discrete geometry of graphs and the differential structure of Wasserstein spaces. To ensure numerical stability and accuracy of numerical behavior, we use extrapolation-type techniques to simulate the viscosity solution on the boundary of density space. By analyzing approximation error of Wasserstein gradient of the viscosity solution, we prove the uniform convergence of the schemes to the original initial value problem. Furthermore, we propose a new compatible boundary assumption on a compact subset of density space, and establish an [math]-error estimate of order one-half. To the best of our knowledge, this is the first result on numerical schemes for HJEs on the Wasserstein space with a graph structure.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"16 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148364943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Log-PDE Methods for Rough Signature Kernels 粗糙签名核的Log-PDE方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-01 DOI: 10.1137/25m1764955

Maud Lemercier, Terry Lyons, Cristopher Salvi

引用次数: 0

A Priori Error Estimates for the [math]-Method for the Flow of Nonsmooth Velocity Fields 非光滑速度场流动[math]-方法的先验误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-01 DOI: 10.1137/25m177432x

Gennaro Ciampa, Tommaso Cortopassi, Gianluca Crippa, Raffaele D’Ambrosio, Stefano Spirito

引用次数: 0

On the Convergence of the Pseudospectral Approximation of Reproduction Numbers for Age-Structured Models 年龄结构模型再现数伪谱近似的收敛性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-07-01 DOI: 10.1137/24m1687224

Simone De Reggi, Francesca Scarabel, Rossana Vermiglio

{"title":"On the Convergence of the Pseudospectral Approximation of Reproduction Numbers for Age-Structured Models","authors":"Simone De Reggi, Francesca Scarabel, Rossana Vermiglio","doi":"10.1137/24m1687224","DOIUrl":"https://doi.org/10.1137/24m1687224","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1073-1094, August 2026. <br/> Abstract. We rigorously investigate the convergence of a new numerical method, recently proposed by the authors, to approximate the reproduction numbers of a large class of age-structured population models with finite age span. The method consists in reformulating the problem in a space of absolutely continuous functions via an integral mapping. For any chosen splitting into birth and transition processes, we first define an operator that maps a generation to the next one (corresponding to the next generation operator in the case of [math]). Then, we approximate the infinite-dimensional operator with a matrix using pseudospectral discretization. In this paper, we prove that the spectral radius of the resulting matrix converges to the true reproduction number, and the (interpolation of the) corresponding eigenvector converges to the associated eigenfunction, with convergence order that depends on the regularity of the model coefficients. Results are confirmed experimentally and applications to epidemiology are discussed.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148365681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability and Convergence of Multi-Product Expansion Splitting Methods with Negative Weights for Semilinear Parabolic Equations 半线性抛物方程负权多积展开分裂方法的稳定性与收敛性

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2026-06-23 DOI: 10.1137/25m1792475

Xianglong Duan, Chaoyu Quan, Jiang Yang, Zijing Zhu

引用次数: 0