Journal of Computational and Applied Mathematics最新文献

{"title":"Reducing overfitting in ResNet with Adaptive Lipschitz regularization","authors":"Manuela Chacon-Chamorro ,&nbsp;Fernando A. Gallego ,&nbsp;J.C. Riano-Rojas","doi":"10.1016/j.cam.2025.116747","DOIUrl":"10.1016/j.cam.2025.116747","url":null,"abstract":"<div><div>This paper introduces Adaptive Lipschitz Bound Regularization with Random Constraints (LBA Regularization), a method designed to mitigate overfitting in residual neural networks by dynamically adjusting the regularization parameter based on the spectral norm of randomly selected layers. Unlike traditional regularization techniques such as L1, L2, Dropout, Early Stopping, and Batch Normalization, LBA leverages an adaptive approach that effectively constrains the Lipschitz bound while maintaining flexibility in deep learning architectures. To substantiate this method, an analysis of the Lipschitz properties in ResNet architectures was performed, offering theoretical insights into their impact on model stability and generalization. The method was evaluated in various neural architectures and datasets, including MNIST, CIFAR-10, and tabular data sets. The results demonstrate that LBA significantly reduces the gap between training and validation accuracy, leading to improved generalization performance. Furthermore, an adversarial robustness analysis against FGSM and PGD attacks confirmed that LBA maintains model stability under adversarial perturbations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116747"},"PeriodicalIF":2.1,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131024","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}

{"title":"Modified homotopy perturbation method for solving singular integral equations of the first kind","authors":"Z.K. Eshkuvatov ,&nbsp;H.X. Mamatova ,&nbsp;Sh. Ismail ,&nbsp;F. Deraman","doi":"10.1016/j.cam.2025.116753","DOIUrl":"10.1016/j.cam.2025.116753","url":null,"abstract":"<div><div>The Homotopy Perturbation Method (HPM) stands out as a robust tool for addressing linear and nonlinear problems across diverse domains of science, engineering, and technology. This paper explores the application of both the standard HPM and modified Homotopy Perturbation Method (MHPM) as semi-analytical solutions for first-kind Cauchy-type singular integral equations (CSIEs). The proposed method effectively transforms singular integral equations into an iterative sequence of algebraic integral equations. The initial iteration introduces unknown coefficients, and a judicious selection of these coefficients often results in the precise solution to the problem. Several examples are presented to display the validity as well as accuracy of the MHPM. Lastly, the obtained results are compared with those derived from HPM, Jacobi polynomials approximation and Taylor approximation. The paper concludes by establishing the stability analysis as well as convergence of the proposed method within a suitable class of functions. It is proven that if characteristic SIEs is considered then the solution obtained by HPM as well as MHPM will coincides with exact solution for any choice of the initial guess.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116753"},"PeriodicalIF":2.1,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131025","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}

{"title":"A fuzzy multiple regression model adopted with locally weighted and interval-valued techniques","authors":"Gholamreza Hesamian ,&nbsp;Arne Johannssen ,&nbsp;Nataliya Chukhrova","doi":"10.1016/j.cam.2025.116751","DOIUrl":"10.1016/j.cam.2025.116751","url":null,"abstract":"<div><div>In this study, a new method for fuzzy linear regression analysis characterized by crisp predictors and fuzzy responses is proposed. The fuzzy responses are decomposed into two separate closed intervals, and then a fuzzy linear regression model is fitted by using the mid-points and ranges of the interval values that result from the center and bounds of the fuzzy responses. The coefficients of the model are estimated within a three-steps procedure by means of the locally weighted estimation procedure. In each step, the unknown bandwidth for identifying the neighboring data points is specified by means of cross-validation. The fuzzy predicted values are then determined via the mid-points and ranges of the predicted interval values. As for performance assessment and comparison with other fuzzy regression models, two approved goodness-of-fit measures are computed. The practical applicability of the proposed model is investigated in the context of a simulation study and four real-data applications. The empirical results reveal the superiority of the introduced regression model compared to its competitors.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116751"},"PeriodicalIF":2.1,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144123251","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}

{"title":"A robust family of optimal fourth-order iteration schemes for multiple roots with applications","authors":"Moin-ud-Din Junjua ,&nbsp;Sunil Kumar ,&nbsp;Rashid Ali","doi":"10.1016/j.cam.2025.116758","DOIUrl":"10.1016/j.cam.2025.116758","url":null,"abstract":"<div><div>This article aims to introduce and analyze a novel class of iterative methods designed specifically to ensure robust and accurate approximation of multiple roots. These methods are derived from Newton-type iterative techniques and are characterized by their higher-order convergence properties. Utilizing the weight function technique, the proposed methods require just three functional evaluations per computation stage to achieve fourth-order convergence. Notably, the theoretical convergence characteristics of the proposed family exhibit symmetrical properties in scenarios involving roots with varying multiplicities. This symmetry motivates a generalized presentation of results confirming the convergence order across different cases. Furthermore, by appropriately selecting free parameters, existing methods can be obtained as specific instances within this broader methodological framework. In contrast to traditional methods, the proposed methods are capable of converging even when <span><math><mrow><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span> or <span><math><mrow><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>→</mo><mn>0</mn></mrow></math></span> near the required root. This notable characteristic broadens the proposed methods’ applicability, enabling them to handle cases where the traditional approaches fail due to the critical points, like the zeros of <span><math><mrow><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span>. The article substantiates its claims through extensive numerical experiments on diverse benchmark problems including the isentropic supersonic flow, Redlich–Kwong equation of state, continuous stirred tank reactor, fractional conversion in a chemical reactor and oscillation problem. Comprehensive comparisons with several established algorithms underscore the superior performance of proposed methods in respect of both CPU efficiency and minimization of absolute residual errors. In addition, to validate the theoretical and numerical results, we compare and visualize the convergence regions of the presented iteration schemes with several existing iteration schemes using diverse nonlinear equations by plotting their basins of attraction in complex plane. The presented iteration methods produce attractor basins in shorter time and exhibit broader convergence regions which confirm their stability and superiority compared to previously known iteration methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116758"},"PeriodicalIF":2.1,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116166","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}

{"title":"Collocation method for Volterra integro-differential equations with piecewise delays","authors":"P. Peyrovan,&nbsp;A. Tari","doi":"10.1016/j.cam.2025.116754","DOIUrl":"10.1016/j.cam.2025.116754","url":null,"abstract":"<div><div>This paper provides a rigorous framework for collocation methods applied to Volterra integro-differential equations (VIDEs) with piecewise linear delays, addressing important gaps in managing discontinuous delay transitions and solution regularity. The proposed method uniquely combines quasi-<span><math><mi>θ</mi></math></span>-invariant meshes with polynomial spline spaces to handle discontinuities induced by delays while preserving optimal convergence. First, the collocation method is extended to VIDEs with piecewise linear delays. Then, the existence and uniqueness of the solution is proved. Convergence analysis is also investigated. At the end, four examples, including two practical examples, are given to illustrate the accuracy and efficiency of the proposed method and confirmation the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116754"},"PeriodicalIF":2.1,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116163","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}

{"title":"Sharp bounds of HH-Mercer inequalities for quadrature formulas in fractional calculus as part of numerical analysis","authors":"Muhammad Aamir Ali ,&nbsp;Jianqiang Xie ,&nbsp;Shigeru Furuichi","doi":"10.1016/j.cam.2025.116748","DOIUrl":"10.1016/j.cam.2025.116748","url":null,"abstract":"<div><div>In this new study, sharp bounds for Hermite–Hadamard–Mercer inequalities are established in the setting of Riemann–Liouville fractional integrals. A modified and sharper version of the Jensen–Mercer inequality is used to establish three distinct error bounds for Hermite–Mercer inequalities. This modified version of the Jensen–Mercer inequality includes a correction factor on the right hand side, which is why it is sharper than the classical Jensen–Mercer inequality. Examples illustrate that the established error bounds for fractional Hermite–Hadamard inequalities, derived using the modified Jensen–Mercer inequality, are sharper than existing ones. This study examines for the first time the influence of the fractional parameter on the integral component of the Hermite–Hadamard inequality, specifically in terms of its convergence of lower and upper bounds. To demonstrate the application of these new results, sharp error bounds for midpoint and trapezoidal inequalities for single time differentiable convex functions are established within the framework of fractional calculus. The error bounds for midpoint and trapezoidal formulas are derived using the modified Jensen–Mercer inequality, providing sharper bounds due to the correction factor on the right hand side. Numerical examples are provided to validate exactness and efficiency of the new results. Finally, applications of the new results are presented for quadrature formulas.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116748"},"PeriodicalIF":2.1,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084445","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}

{"title":"Entropy-based feature selection for capturing impacts in Earth system models with abrupt forcing","authors":"Jerry Watkins ,&nbsp;Luca Bertagna ,&nbsp;Graham Harper ,&nbsp;Andrew Steyer ,&nbsp;Irina Tezaur ,&nbsp;Diana Bull","doi":"10.1016/j.cam.2025.116724","DOIUrl":"10.1016/j.cam.2025.116724","url":null,"abstract":"<div><div>This paper presents the development of a new entropy-based feature selection method for identifying and quantifying impacts. Here, impacts are defined as statistically significant differences in spatio-temporal fields when comparing datasets with and without an external forcing in an Earth system model. Temporal feature selection is performed by first computing the cross-fuzzy entropy to quantify similarity of patterns between two datasets and then applying changepoint detection to identify regions of statistically constant entropy. The method is used to capture temperate north surface cooling from a 9-member simulation ensemble of the Mt. Pinatubo volcanic eruption, which injected 10 Tg of SO₂ into the stratosphere. The results estimate a mean difference decrease in near surface air temperature of <span><math><mrow><mo>−</mo><mn>0</mn><mo>.</mo><mn>560</mn></mrow></math></span> K with a 99% confidence interval between <span><math><mrow><mo>−</mo><mn>0</mn><mo>.</mo><mn>864</mn></mrow></math></span> K and <span><math><mrow><mo>−</mo><mn>0</mn><mo>.</mo><mn>257</mn></mrow></math></span> K between April and November of 1992, one year following the eruption. A sensitivity analysis with decreasing SO₂ injection revealed that the impact is statistically significant at 5 Tg but not at 3 Tg. Using identified features, a dependency graph model based on a 9-day lag had significantly fewer nodes than a graph based on monthly means. This demonstrates our method’s ability to perform dimension reduction while still uncovering source-to-impact pathways.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116724"},"PeriodicalIF":2.1,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084448","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}

{"title":"Convergence analysis of semi-smooth Newton method for mixed FEM approximations of dynamic two-body contact and crack problems","authors":"Victor A. Kovtunenko ,&nbsp;Yves Renard","doi":"10.1016/j.cam.2025.116722","DOIUrl":"10.1016/j.cam.2025.116722","url":null,"abstract":"<div><div>A class of elastodynamic problems describing contact between two deformable bodies as well as non-penetrating cracks in a single body is considered in the framework of FEM approximation. For time discretization, the Hilber–Hughes–Taylor (HHT-<span><math><mi>α</mi></math></span>) method extending Newmark schemes is incorporated. Using mixed variational formulation of the fully discrete contact problem, a semi-smooth Newton method of solution is provided with the locally super-linear convergence. An equivalent primal–dual active set algorithm validates monotone properties of global convergence for the Newton iterates provided by M-matrix property. Numerical solution of the Signorini contact with rigid obstacle is presented for isotropic body in 2D using benchmark and moving load experiment.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116722"},"PeriodicalIF":2.1,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084446","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}

{"title":"An adaptive finite element DtN method for the acoustic transmission problem","authors":"Lei Lin,&nbsp;Junliang Lv,&nbsp;Jiahui Gao","doi":"10.1016/j.cam.2025.116725","DOIUrl":"10.1016/j.cam.2025.116725","url":null,"abstract":"<div><div>In the present paper, we consider the scattering of a time-harmonic acoustic incident wave by the bounded penetrable obstacle. By introducing the Dirichlet-to-Neumann (DtN) operator, the model is formulated as a transmission boundary value problem of acoustics. An a posteriori error estimate is derived for the finite element method with the truncated DtN operator, where the a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN operator. Based on the a posteriori error, an adaptive finite element algorithm is designed for solving the acoustic transmission problem. Numerical experiments are also presented to demonstrate the effectiveness and robustness of our adaptive method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116725"},"PeriodicalIF":2.1,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084444","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}

{"title":"Mixtures of common factor analyzers using the restricted multivariate skew-t distribution for clustering high-dimensional data with missing values","authors":"Wan-Lun Wang ,&nbsp;Luis M. Castro ,&nbsp;Shi-Xiu Yu ,&nbsp;Tsung-I Lin","doi":"10.1016/j.cam.2025.116708","DOIUrl":"10.1016/j.cam.2025.116708","url":null,"abstract":"<div><div>Mixtures of common restricted skew-<span><math><mi>t</mi></math></span> factor analyzers (MCrstFA) have emerged as a parsimonious and practical approach for the model-based clustering of high-dimensional data with asymmetric features and outlying observations in one or more heterogeneous populations. However, missing data has become a ubiquitous problem that frequently adds complexity to the analyses for practitioners. Most existing tools are not adaptable to data with missing values, which is a significant reason for this complexity. This paper proposes an extension of the MCrstFA framework that allows the analyst to parsimoniously model data with missing values, skewness, heavy tails, and multimodality simultaneously. Under the missing at random (MAR) mechanism for nonresponses, a computationally feasible expectation conditional maximization either (ECME) algorithm is developed for computing maximum likelihood (ML) estimates of model parameters. The estimation procedure enables the automatic imputation of missing values and the prediction of unobserved factor scores. To assess the precision of the ML estimators, an information matrix-based approach is employed to approximate the asymptotic covariance matrix of the estimators. Numerical results obtained from the analysis of simulated and real datasets illustrate the effectiveness of the proposed methodology.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"471 ","pages":"Article 116708"},"PeriodicalIF":2.1,"publicationDate":"2025-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084447","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}