Journal of Computational and Applied Mathematics最新文献_第3页

Approximation capabilities of certain nonlinear neural network operators 一类非线性神经网络算子的逼近能力

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-13 DOI: 10.1016/j.cam.2026.117452

Sachin Saini, Uaday Singh

{"title":"Approximation capabilities of certain nonlinear neural network operators","authors":"Sachin Saini, Uaday Singh","doi":"10.1016/j.cam.2026.117452","DOIUrl":"10.1016/j.cam.2026.117452","url":null,"abstract":"<div><div>In this paper, a new family of nonlinear neural network operators with a single hidden layer has been introduced for a class of continuous functions and Lebesgue integrable functions on a compact interval. We used specific activation functions constructed using a class of sigmoidal functions. The convergence of these operators is examined, and we establish both pointwise and uniform approximation theorems for the functions in the class of continuous functions <span><math><mrow><mi>C</mi><mo>(</mo><mi>I</mi><mo>)</mo></mrow></math></span>, <span><math><mrow><mi>I</mi><mo>=</mo><mo>[</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>]</mo></mrow></math></span>. We also extend the study for the class of Lebesgue integrable functions <span><math><mrow><msup><mi>L</mi><mi>p</mi></msup><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow></mrow></math></span> for <em>p</em> ≥ 1. Investigation of these nonlinear operators provides valuable insights into their generalization ability and practical applications in signal processing. We also discuss some examples, quantitative estimates, and graphical representations to highlight the applications.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117452"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387182","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

Can symmetric positive definite (SPD) coarse spaces perform well for indefinite Helmholtz problems? 对称正定（SPD）粗空间能否很好地解决不确定亥姆霍兹问题？

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-11 DOI: 10.1016/j.cam.2026.117403

Victorita Dolean , Mark Fry , Matthias Langer

{"title":"Can symmetric positive definite (SPD) coarse spaces perform well for indefinite Helmholtz problems?","authors":"Victorita Dolean , Mark Fry , Matthias Langer","doi":"10.1016/j.cam.2026.117403","DOIUrl":"10.1016/j.cam.2026.117403","url":null,"abstract":"<div><div>Wave propagation problems governed by the Helmholtz equation remain among the most challenging in scientific computing, due to their indefinite nature. Domain decomposition methods with spectral coarse spaces have emerged as some of the most effective preconditioners, yet their theoretical guarantees often lag behind practical performance. In this work, we introduce and analyse the Δ<sub><em>k</em></sub>-GenEO coarse space within the two-level additive Schwarz preconditioners for heterogeneous Helmholtz problems. This is an adaptation of the Δ-GenEO coarse space. Our results sharpen the <em>k</em>-explicit conditions for GMRES convergence, reducing the restrictions on the subdomain size and eigenvalue threshold. This narrows the long-standing gap between pessimistic theory and empirical evidence, and reveals why GenEO spaces based on SPD (symmetric positive definite) eigenvalue problems remain surprisingly effective despite their apparent limitations. Numerical experiments confirm the theory, demonstrating scalability, robustness to heterogeneity for low to moderate frequencies (while experiencing limitations in the high frequency cases), and significantly milder coarse-space growth than conservative estimates predict.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117403"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387185","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

On reducibility of ADMM based on degenerate proximal point analysis 基于退化近端点分析的ADMM可约性研究

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-27 DOI: 10.1016/j.cam.2026.117531

Feng Xue

引用次数: 0

A new strong equilibrium of multi-leader-multi-follower games: Characterization and essential stability 多领导-多随从博弈的一种新的强均衡：特征和本质稳定性

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-24 DOI: 10.1016/j.cam.2026.117524

Yunbing Li , Wensheng Jia , Shuwen Xiang

引用次数: 0

A transported PDF modeling method applied to one-dimensional stochastic Burgers equation 一种用于一维随机Burgers方程的传输PDF建模方法

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-20 DOI: 10.1016/j.cam.2026.117464

Yize Wang , Li Yuan

{"title":"A transported PDF modeling method applied to one-dimensional stochastic Burgers equation","authors":"Yize Wang , Li Yuan","doi":"10.1016/j.cam.2026.117464","DOIUrl":"10.1016/j.cam.2026.117464","url":null,"abstract":"<div><div>In this paper we apply the transported probability density function (PDF) method to model the Burgers turbulence governed by the one-dimensional Burgers equation with a stochastic external force and random initial data. The PDF modeling method can provide the mean and high order moments of the random solution variable which are useful for the characterization of Burgers turbulence. Firstly, an exact one-point PDF transport equation is derived from the Burgers equation with a stochastic external force, and then the conditional advection and diffusion terms are modeled for closure by using two respective models. Secondly, three numerical methods are employed to solve the modeled PDF transport equation: the mesh-based Lagrangian particle Monte Carlo (MC) method, the original quadrature method of moments (QMOM), and the linear QMOM (LQMOM) as modified in this work. The numerical tests verify the viability of using the PDF modeling method to study Burgers turbulence and show that the MC method, LQMOM and QMOM can yield results comparable to the DNS solution, and the LQMOM is more efficient than the QMOM and MC method. However, the MC method has less dissipation for turbulence in high wavenumber regimes.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117464"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387128","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

Existence and continuity theorems of equilibrium solutions of multi-objective leader-follower games with fuzzy payoffs 具有模糊收益的多目标leader-follower博弈均衡解的存在性和连续性定理

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-24 DOI: 10.1016/j.cam.2026.117518

Li Zhou , Wensheng Jia

引用次数: 0

Image recovery via modified Dai-Kou method for constrained system of nonlinear equations 基于改进Dai-Kou法的约束非线性方程组图像恢复

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-24 DOI: 10.1016/j.cam.2026.117537

Kabiru Ahmed , Mohammed Yusuf Waziri , Abubakar Sani Halilu , Salisu Murtala

{"title":"Image recovery via modified Dai-Kou method for constrained system of nonlinear equations","authors":"Kabiru Ahmed , Mohammed Yusuf Waziri , Abubakar Sani Halilu , Salisu Murtala","doi":"10.1016/j.cam.2026.117537","DOIUrl":"10.1016/j.cam.2026.117537","url":null,"abstract":"<div><div>In this paper, a modified version of the method by Dai and Kou for unconstrained optimization is presented for solving constrained nonlinear system of equations with applications to blurry image recovery. To develop the scheme, an effective choice for the Dai-Kou parameter <em>τ<sub>k</sub></em>, which has been declared a subject of research, was obtained by conducting singular value analysis and minimizing upper bound of the condition number of the search direction matrix of the classical Dai-Kou scheme. The backtracking linesearch presented by Li and Li is used to obtain step-size in the algorithm. The scheme satisfies the vital condition for analyzing global convergence. It is also suitable for solving some large-scale nonsmooth problems since it avoids computing the Jacobian. Mild conditions are employed to prove the schemes’ global convergence, while numerical experiments with related methods are carried out to illustrate its effectiveness for solving constrained nonlinear system of equations. The method was also tested with two effective schemes in the literature to illustrate its effectiveness in image de-blurring problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117537"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387001","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

Smooth-like lower order penalty approach for solving second-order cone mixed complementarity problems 求解二阶锥混合互补问题的光滑低阶惩罚方法

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-24 DOI: 10.1016/j.cam.2026.117513

Zijun Hao , Qiong Wu, Chunmin Zhao

引用次数: 0

Machine learning analysis of thermal and solutal transport rates for Eyring-Powell magneto-nanomaterial model (EPMNM) Eyring-Powell磁纳米材料模型（EPMNM）热输运率和溶质输运率的机器学习分析

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-08 DOI: 10.1016/j.cam.2026.117417

Sana Jabeen , Muhammad , Masood Khan , Syed Modassir Hussain

{"title":"Machine learning analysis of thermal and solutal transport rates for Eyring-Powell magneto-nanomaterial model (EPMNM)","authors":"Sana Jabeen , Muhammad , Masood Khan , Syed Modassir Hussain","doi":"10.1016/j.cam.2026.117417","DOIUrl":"10.1016/j.cam.2026.117417","url":null,"abstract":"<div><div>Artificial intelligence (AI), a revolutionary force in modern scientific research across various domains, has the potential to provide new solutions for highly complex and challenging physical models. This paper investigates the incompressible flow of an Eyring-Powell magneto-nanofluid model (EPMNM) over a stretching surface. The effects of thermal and solutal mechanisms are analyzed by incorporating variable thermal conductivity, mass diffusivity, chemical reactions, and heat sources. The Buongiorno model is employed to capture the influence of nanofluids through thermophoresis and Brownian motion. The relevant transformations convert the governing PDEs into coupled nonlinear ODEs. The numerical solution is obtained using the fourth-order Runge-Kutta-Fehlberg method in conjunction with the shooting technique. Furthermore, the Levenberg-Marquardt Neural Network Algorithm (LMNNA) is employed in an intelligent, ANN-based numerically validated solver to analyze the resulting fluid model. The BVP4C approach generated a chart displaying the behavior of the friction drag, Local Motile Density Number (LMDN), thermal, and solutal transportation rates. A dataset for various scenarios of the intriguing and comprehensive nanofluid model has been produced by exploiting BVP4C. The strengths of the machine learning analysis using LMNNA are then investigated through physical quantities such as SFC, LNN, LSHN, and LMDN. Datasets comprising 60 and 45 outcomes are categorized into three groups: training (70%), validation (15%), and testing (15%). The hidden layer consists of ten neurons. Tables 4 through 7 present the ANN predictions alongside the numerical values for SFC, LNN, LSHN, and LMDN. The accuracy of the developed neural network for these physical quantities is assessed using regression analysis and mean squared error.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117417"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387118","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

Extended block Krylov subspace approaches for solving large-scale linear system of fractional DEs 求解分数阶微分方程大规模线性系统的扩展块Krylov子空间方法

IF 2.6 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2026-10-01 Epub Date: 2026-02-14 DOI: 10.1016/j.cam.2026.117455

Lakhlifa Sadek , Hamad Talibi Alaoui , Ahmad Sami Bataineh , Ishak Hashim

{"title":"Extended block Krylov subspace approaches for solving large-scale linear system of fractional DEs","authors":"Lakhlifa Sadek , Hamad Talibi Alaoui , Ahmad Sami Bataineh , Ishak Hashim","doi":"10.1016/j.cam.2026.117455","DOIUrl":"10.1016/j.cam.2026.117455","url":null,"abstract":"<div><div>This study addresses the numerical solution of large-scale linear systems of fractional differential equations (LSFDEs) featuring a low-rank constant term a class of problems not previously investigated in the literature. We propose two novel numerical approaches for solving such systems. The first method exploits the integral representation of the exact solution and employs a Krylov-based approximation to compute the action of the matrix Mittag–Leffler function on a block of vectors. The second approach projects the original high-dimensional fractional system onto an extended block Krylov subspace, reducing it to a significantly smaller fractional differential system. This reduced system is then solved using either a tailored implementation of the Grünwald-Letnikov scheme or a fractional backward differentiation formula, both adapted to the projected setting. The resulting low-rank approximate solution is iteratively refined by expanding the projection subspace until a prescribed tolerance is achieved. We derive explicit expressions for the residual and error norms and establish associated convergence estimates. To validate the computational efficiency and accuracy of the proposed methods, we conduct extensive numerical experiments on several benchmark problems. The results demonstrate that our approaches substantially reduce computational time while maintaining high numerical precision, outperforming existing conventional solvers for large-scale fractional systems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117455"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387124","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