Advances in Computational Mathematics最新文献_第3页

Theoretical and numerical analysis of a nonlinear double-phase variable exponent model for image contrast enhancement 图像对比度增强的非线性双相变指数模型的理论和数值分析

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-14 DOI: 10.1007/s10444-026-10334-3

Abderrahim Charkaoui, Anouar Ben-Loghfyry, Shengda Zeng

{"title":"Theoretical and numerical analysis of a nonlinear double-phase variable exponent model for image contrast enhancement","authors":"Abderrahim Charkaoui, Anouar Ben-Loghfyry, Shengda Zeng","doi":"10.1007/s10444-026-10334-3","DOIUrl":"10.1007/s10444-026-10334-3","url":null,"abstract":"<div><p>This study introduces a novel nonlinear parabolic equation characterized by a variable growth structure, specifically designed for image restoration and enhancement. Our approach builds upon classical models that employ variable exponent operators, extending their capabilities by incorporating a newly developed nonlinear operator featuring a <i>double-phase</i> flux with variable growth. This novel formulation allows for greater adaptability in modeling complex image structures while maintaining key elements like textures and corners. To establish a solid theoretical foundation, we begin by investigating the solvability of the proposed model. Utilizing the framework of variable exponent Lebesgue and Sobolev spaces, we develop an appropriate functional setting that enables rigorous mathematical analysis. The initial focus of our study is to ensure the well-posedness of the model. As a key result, we employ an approximation approach to prove the existence of a positive weak solution called solution obtained as limit of approximations (SOLA). Beyond theoretical considerations, we validate our model through practical applications in image processing. We conduct extensive numerical experiments on grayscale images to assess its performance in denoising and contrast enhancement. Additionally, we conducted evaluations on a collection of magnetic resonance imaging (MRI) scans, further demonstrating its applicability in medical imaging. Our experimental findings demonstrate that the proposed model consistently outperforms current state-of-the-art approaches, achieving enhanced computational efficiency and greater robustness while delivering superior results in both qualitative visual assessment and quantitative evaluation metrics. The findings emphasize the effectiveness of our model as a promising approach for tackling advanced image restoration and enhancement problems.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148431996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

A stabilized trace FEM for surface Cahn–Hilliard equations: analysis and simulations 表面Cahn-Hilliard方程的稳定轨迹有限元分析与仿真

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-13 DOI: 10.1007/s10444-026-10331-6

Deepika Garg, Maxim Olshanskii

引用次数: 0

Pointwise error estimates for Legendre spectral differentiation of functions with limited regularity in fractional spaces 分数空间中有限正则函数的Legendre谱微分的点误差估计

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-13 DOI: 10.1007/s10444-026-10328-1

Ruiyi Xie, Wenjie Liu, Boying Wu

引用次数: 0

A meshfree method for eigenvalues of differential operators on surfaces, including Steklov problems 曲面上微分算子特征值的无网格方法，包括Steklov问题

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-09 DOI: 10.1007/s10444-026-10335-2

Daniel R. Venn, Steven J. Ruuth

{"title":"A meshfree method for eigenvalues of differential operators on surfaces, including Steklov problems","authors":"Daniel R. Venn, Steven J. Ruuth","doi":"10.1007/s10444-026-10335-2","DOIUrl":"10.1007/s10444-026-10335-2","url":null,"abstract":"<div><p>We present and study techniques for investigating the spectra of linear differential operators on surfaces and flat domains using symmetric meshfree methods: meshfree methods that arise from finding norm-minimizing Hermite–Birkhoff interpolants in a Hilbert space. Meshfree methods are desirable for surface problems due to the increased difficulties associated with mesh creation and refinement on curved surfaces. While meshfree methods have been used for solving a wide range of partial differential equations (PDEs) in recent years, the spectra of operators discretized using radial basis functions (RBFs) often suffer from the presence of non-physical eigenvalues (spurious modes). This makes many RBF methods unhelpful for eigenvalue problems. We provide rigorously justified processes for finding eigenvalues based on results concerning the norm of the solution in its native space; specifically, only PDEs with solutions in the native space produce numerical solutions with bounded norms as the fill distance approaches zero. For certain problems, we prove that eigenvalue and eigenfunction estimates converge at a high-order rate. The technique we present is general enough to work for a wide variety of problems, including Steklov problems, where the eigenvalue parameter is in the boundary condition. Numerical experiments for a mix of standard and Steklov eigenproblems on surfaces with and without boundary, as well as flat domains, are presented, including a Steklov–Helmholtz problem.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148409137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Multivariate rational approximation via low-rank tensors and the p-AAA algorithm 基于低秩张量和p-AAA算法的多元有理逼近

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-08 DOI: 10.1007/s10444-026-10330-7

Linus Balicki, Serkan Gugercin

{"title":"Multivariate rational approximation via low-rank tensors and the p-AAA algorithm","authors":"Linus Balicki, Serkan Gugercin","doi":"10.1007/s10444-026-10330-7","DOIUrl":"10.1007/s10444-026-10330-7","url":null,"abstract":"<div><p>Approximations based on rational functions are widely used in various applications across computational science and engineering. For univariate functions, the adaptive Antoulas–Anderson algorithm (AAA), which uses the barycentric form of a rational approximant, has established itself as a powerful tool for efficiently computing such approximations. The p-AAA algorithm, an extension of the AAA algorithm specifically designed to address multivariate approximation problems, has been recently introduced. A common challenge in multivariate approximation methods is that multivariate problems with a large number of variables often pose significant memory and computational demands. To tackle this hurdle in the setting of p-AAA, we first introduce barycentric forms that are expressed via separable functions. This then leads to the low-rank p-AAA algorithm which leverages low-rank tensor decompositions in the setting of barycentric rational approximations. We discuss various theoretical and practical aspects of the proposed computational framework and showcase its effectiveness on four numerical examples. We focus specifically on applications in parametric reduced-order modeling for which higher-dimensional data sets can be tackled effectively with our novel procedure.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10330-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148408866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An a priori (L^{2})–norm error estimate of the hybrid high-order method for a class of strongly monotone nonlinear elliptic problems 一类强单调非线性椭圆型问题混合高阶方法的先验$$L^{2}$$ -范数误差估计

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-06 DOI: 10.1007/s10444-026-10329-0

Rommel Bustinza, Jonathan Munguia-La-Cotera

引用次数: 0

Kernel-based greedy approximation of parametric elliptic boundary value problems 参数椭圆边值问题的核贪心逼近

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-03 DOI: 10.1007/s10444-026-10323-6

Bernard Haasdonk, Tizian Wenzel, Gabriele Santin

{"title":"Kernel-based greedy approximation of parametric elliptic boundary value problems","authors":"Bernard Haasdonk, Tizian Wenzel, Gabriele Santin","doi":"10.1007/s10444-026-10323-6","DOIUrl":"10.1007/s10444-026-10323-6","url":null,"abstract":"<div><p>We recently introduced a scale of kernel-based greedy schemes for approximating the solutions of elliptic boundary value problems. The procedure is based on a generalized interpolation framework in reproducing kernel Hilbert spaces and was coined PDE-<span>(beta )</span>-greedy procedure, where the parameter <span>(beta ge 0 )</span> is used in a greedy selection criterion and steers the degree of function adaptivity. Algebraic convergence rates have been obtained for Sobolev-space kernels and solutions of finite smoothness. We now report a result of exponential convergence rates for the case of an infinitely smooth kernel and infinitely smooth solutions. We furthermore extend the approximation scheme to the case of parametric partial differential equations by the use of position-parameter product kernels. In the surrogate modelling context, the resulting approach can be interpreted as an <i>a priori</i> model reduction approach, as no solution snapshots need to be precomputed. Numerical results show the efficiency of the approximation procedure for problems which occur as challenges for other parametric model order reduction procedures: non-affine geometry parametrizations, moving sources, or high-dimensional domains.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10323-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A straightforward discrete energy technique for weighted and shifted backward differentiation formulas up to fifth order 一种直接的离散能量技术，用于加权和倒移到五阶的微分公式

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-07-01 DOI: 10.1007/s10444-026-10325-4

Yuanyuan Kang, Dongqian Li, Yin Yang

引用次数: 0

Randomized gradient descent method for solving the large-scale inverse eigenvalue problem arising from the fractional order control system 求解分数阶控制系统大规模特征值反问题的随机梯度下降法

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-06-30 DOI: 10.1007/s10444-026-10324-5

Bin-Xin He, Hao Liu, Xiao-Ping Chen

{"title":"Randomized gradient descent method for solving the large-scale inverse eigenvalue problem arising from the fractional order control system","authors":"Bin-Xin He, Hao Liu, Xiao-Ping Chen","doi":"10.1007/s10444-026-10324-5","DOIUrl":"10.1007/s10444-026-10324-5","url":null,"abstract":"<div><p>The large-scale inverse eigenvalue problem arising from the fractional order control system presents mathematical and computational challenges due to its expensive computational costs and nonconvex nature. Considering that a smaller feedback control force implies less energy consumption and lower noise influence in control applications of the actual system, we transform the large-scale inverse eigenvalue problem into a matrix-based nonconvex optimization problem, which transcends the limitations of the vector-based optimization problem. To solve this nonconvex optimization problem, we propose an effective probability criterion and present a matrix-based randomized gradient descent method. The proposed method operates directly on the matrix form without vectorization and only needs to update a single row of the parameter matrix per iteration in practice, which makes it more suitable for the computation of large-scale nonconvex optimization problem. Then, we prove the smoothness of the objective function and further analyze the convergence of the proposed method. Finally, numerical experiments demonstrate the validity of our approach against traditional optimization-based methods and confirm the effectiveness of our approach in solving large-scale inverse eigenvalue problem arising from the fractional order control system.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

A parameterized block preconditioner for solving a class of complex symmetric linear systems 求解一类复对称线性系统的参数化块预调节器

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-06-30 DOI: 10.1007/s10444-026-10326-3

Meng-Yao Li, Bo Wu

引用次数: 0