Journal of Computational and Applied Mathematics最新文献

{"title":"Regularized Nesterov’s accelerated damped BFGS method for stochastic optimization","authors":"Siwakon Suppalap ,&nbsp;Dawrawee Makmuang ,&nbsp;Vipavee Damminsed ,&nbsp;Rabian Wangkeeree","doi":"10.1016/j.cam.2025.116616","DOIUrl":"10.1016/j.cam.2025.116616","url":null,"abstract":"<div><div>A regularization term is introduced into the approximate Hessian update in the stochastic Broyden–Fletcher–Goldfarb–Shanno (BFGS) method for convex stochastic optimization problems to help avoid near-singularity issues. Additionally, Nesterov acceleration, with a momentum coefficient that dynamically adjusts between a constant value and zero based on the objective function, has been incorporated to enhance convergence speed. However, the inflexibility of the constant momentum coefficient still may lead to overshooting problems, and evaluating objective functions on large datasets is computationally costly. Moreover, this approach presents challenges in solving nonconvex optimization problems. To address these challenges, we propose a regularized stochastic BFGS method that integrates Nesterov acceleration with an adaptive momentum coefficient designed for solving nonconvex stochastic optimization problems. This coefficient adjusts flexibly between a decreasing value and zero based on selected dataset samples, helping to avoid overshooting problems and reduce computational costs. We demonstrated almost sure convergence to stationary points and analyze the complexity. Numerical results on convex and nonconvex classification problems using a support vector machine show that our method outperforms existing approaches.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116616"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580628","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 discrete-time queue with service time adjustments and general retrial times","authors":"Iván Atencia,&nbsp;José Luis Galán-García,&nbsp;Yolanda Padilla-Domínguez,&nbsp;Pedro Rodríguez-Cielos","doi":"10.1016/j.cam.2025.116605","DOIUrl":"10.1016/j.cam.2025.116605","url":null,"abstract":"<div><div>This paper examines a discrete-time retrial queueing system where incoming customers can either choose a last-come, first-served (LCFS) discipline or enter an orbit. It accounts for the possibility of varying service times, which follow an arbitrary distribution, and the retrial times are also governed by an arbitrary distribution. The underlying Markov chain of the system has been analyzed, leading to the derivation of the generating function for the number of customers in both the orbit and the overall system, along with their expected values. The paper also establishes the stochastic decomposition law and, as an application, provides bounds for the difference between the steady-state distributions of the system in question and its standard equivalent. Recursive formulas for determining the steady-state distribution of customers in the orbit and the system are presented. The paper derives the distribution of the time a customer spends at the server and, consequently, the distribution of service times subject to possible variations. A detailed analysis of the time a customer spends in the orbit is also conducted. Finally, numerical examples are included to demonstrate how key parameters impact various system characteristics, with the main contributions of the research summarized in the conclusion.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116605"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143571484","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":"Dual Neural Network (DuNN) method for elliptic partial differential equations and systems","authors":"Min Liu ,&nbsp;Zhiqiang Cai ,&nbsp;Karthik Ramani","doi":"10.1016/j.cam.2025.116596","DOIUrl":"10.1016/j.cam.2025.116596","url":null,"abstract":"<div><div>This paper presents the Dual Neural Network (DuNN) method, a physics-driven numerical method designed to solve elliptic partial differential equations and systems using deep neural network functions and a dual formulation. The underlying elliptic problem is formulated as an optimization of the complementary energy functional in terms of the dual variable, where the Dirichlet boundary condition is weakly enforced in the formulation. To accurately evaluate the complementary energy functional, we employ a novel discrete divergence operator. This discrete operator preserves the underlying physics and naturally enforces the Neumann boundary condition without penalization. For problems without reaction term, we propose an outer-inner iterative procedure that gradually enforces the equilibrium equation through a pseudo-time approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116596"},"PeriodicalIF":2.1,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143591914","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":"Spectral approximated superconvergent method for nonlinear Volterra Hammerstein integral equations with weakly singular kernels","authors":"Samiran Chakraborty ,&nbsp;Shivam Kumar Agrawal ,&nbsp;Gnaneshwar Nelakanti","doi":"10.1016/j.cam.2025.116601","DOIUrl":"10.1016/j.cam.2025.116601","url":null,"abstract":"<div><div>In this paper, we apply Jacobi spectral Galerkin and multi-Galerkin methods using Kumar–Sloan technique for obtaining approximations of weakly singular Volterra integral equation of Hammerstein type and obtain superconvergence results. We derive the enhanced superconvergence results for the Kumar–Sloan approximation based on Galerkin and multi-Galerkin methods in both cases: when the exact solution is smooth and when the exact solution is non-smooth, in both infinity and weighted-<span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norms. We conclude that without the need for the iterated versions, we achieve superconvergence rates as high as the superconvergence rates of iterated Galerkin and iterated multi-Galerkin methods. The numerical results are presented to demonstrate the theoretical ones.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"467 ","pages":"Article 116601"},"PeriodicalIF":2.1,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580625","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":"Nonparametric estimations of quantile residual life function with censored length-biased data","authors":"Hongping Wu ,&nbsp;Ang Shan ,&nbsp;Xiaosha Li","doi":"10.1016/j.cam.2025.116606","DOIUrl":"10.1016/j.cam.2025.116606","url":null,"abstract":"<div><div>In biomedical studies, the median or quantile residual life is often treated as an important quantitative measure for the length of individuals’ residual life besides the mean residual life. In this paper, two nonparametric estimating methods for quantile residual life function are developed with censored length-biased data, and they are constructed based on the moment-based estimation idea and martingale theory, respectively. In particular, the proposed martingale-based estimating method can avoid estimating the survival function of the target population or the right-censoring variable. The consistency and weak convergence of two estimations are also established. In order to evaluate their performance and accuracy in a finite sample, a series of small simulation studies are carried out, too. Finally, an analysis of the famous Channing House data is provided.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116606"},"PeriodicalIF":2.1,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551032","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":"General K-order Franklin wavelet method for numerical solution of integral equations","authors":"Jiayi Zhu,&nbsp;Kang Huang,&nbsp;Yuanjie Xian","doi":"10.1016/j.cam.2025.116607","DOIUrl":"10.1016/j.cam.2025.116607","url":null,"abstract":"<div><div>The classical Franklin system is a complete orthonormal set of piecewise linear continuous functions using Haar wavelet collocation points. This paper defines the general K-order Franklin function and introduces the general K-order Franklin wavelet method for solving Fredholm and Volterra integral equations. The method is also applied to solve mixed nonlinear Fredholm–Volterra integral equations. The general K-order Franklin wavelet method, like the higher-order Haar wavelet method, is a collocation method. Its advantage of not requiring constraint equations makes it easier to extend to higher orders, resulting in faster convergence. Several examples are provided to illustrate the reliability and effectiveness of the proposed method. Compared to the fourth-order convergence rate of the higher-order Haar wavelet method, the proposed general K-order Franklin wavelet method achieves a sixth-order convergence rate, improving both the rate of convergence and reducing the absolute error.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116607"},"PeriodicalIF":2.1,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551035","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":"Reconstructing algebraic functions from a nonconforming exponential weighted enriched finite element","authors":"Francesco Dell’Accio ,&nbsp;Allal Guessab ,&nbsp;Gradimir V. Milovanović ,&nbsp;Federico Nudo","doi":"10.1016/j.cam.2025.116603","DOIUrl":"10.1016/j.cam.2025.116603","url":null,"abstract":"<div><div>The reconstruction of functions is a fundamental task in various applications, ranging from computer graphics to remote sensing. This paper addresses the challenge of function reconstruction in scenarios where, instead of pointwise function evaluations, only a set of integrals over specific lines is available. We propose a novel method based on a one-parameter family of weighted finite elements that incorporates exponential Hermite weight functions within bounded domains. Numerical experiments demonstrate that the proposed approach significantly improves computational efficiency and accuracy in function reconstruction compared to the classical Crouzeix–Raviart finite element.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116603"},"PeriodicalIF":2.1,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A method for solving ill-conditioned separable nonlinear least squares problems and its application","authors":"Luyao Wang ,&nbsp;Guolin Liu ,&nbsp;Yang Chen ,&nbsp;Huadong Ma","doi":"10.1016/j.cam.2025.116624","DOIUrl":"10.1016/j.cam.2025.116624","url":null,"abstract":"<div><div>For ill-conditioned separable nonlinear least squares problems, the LM (Levenberg-Marquardt) iteration method based on the VP (Variable Projection) algorithm and SVD (Singular Value Decomposition) for solving nonlinear parameters is explored in this paper, and a ridge estimation is proposed based on the TSVD (Truncated Singular Value Decomposition) and MSVD (Modified Singular Value Decomposition) methods to solve linear parameters. It is proved that the LM method based on SVD and the improved algorithm based on TSVD and MSVD can overcome the ill-conditioning of the matrix to a certain extent and enhance the reliability of parameter estimation through Mackey-Glass time series simulation and height anomaly fitting experiments. TSVD, MSVD and improved algorithm are compared and analyzed in terms of the accuracy and stability of parameter estimation and the curve fitting effect in the Mackey-Glass time series simulation experiment. The height anomaly fitting experiment verifies the feasibility and applicability of the algorithm in such practical problems. The experimental results show that the improved algorithm based on TSVD and MSVD enables the parameter estimation to be more stable, and the parameter values calculated by the algorithm bring about a better goodness of fit and fitting effect of the model.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116624"},"PeriodicalIF":2.1,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551037","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 new double relaxed inertial viscosity-type algorithm for split equilibrium problems and its application to detecting osteoporosis health problems","authors":"Watcharaporn Yajai ,&nbsp;Wongthawat Liawrungrueang ,&nbsp;Watcharaporn Cholamjiak","doi":"10.1016/j.cam.2025.116602","DOIUrl":"10.1016/j.cam.2025.116602","url":null,"abstract":"<div><div>This article proposes a new double relaxed inertial viscosity-type algorithm for solving split equilibrium problems; this algorithm is flexible to use by the relaxed extrapolation parameters in real numbers. We obtain a strong convergence theorem under suitable assumptions of two bifunctions in real Hilbert spaces. In data classification, we apply our proposed algorithm for finding optimal output weight in an extreme learning machine. The primary features of the Osteoporosis dataset from Harvard Dataverse are used for the algorithm’s experiments. The right extrapolation parameters show that the algorithm converges faster than the standard algorithm. The comparison with the existing algorithm is demonstrated for our proposed algorithm’s high efficiency. Finally, our algorithm’s accuracy and loss plots are presented, obtaining our good-fitting model.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116602"},"PeriodicalIF":2.1,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519490","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 compact scheme for the Munk boundary-layer equation in one dimension","authors":"M. Ben-Artzi ,&nbsp;J.-P. Croisille ,&nbsp;D. Fishelov","doi":"10.1016/j.cam.2025.116595","DOIUrl":"10.1016/j.cam.2025.116595","url":null,"abstract":"<div><div>In this paper, we introduce a two-scale compact finite difference scheme for the equation <span><span><span>(MK-1D)</span><span><math><mfenced><mrow><mtable><mtr><mtd></mtd><mtd><mo>−</mo><mi>β</mi><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mi>u</mi><mo>+</mo><mi>ɛ</mi><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></msup><mi>u</mi><mo>=</mo><mi>f</mi><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>u</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>=</mo><mi>u</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>.</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>This equation serves as a model for the nonlinear barotropic equation (NB) governing oceanic flows. <span><span><span>(NB)</span><span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>Δ</mi><mi>ψ</mi><mo>+</mo><msup><mrow><mo>∇</mo></mrow><mrow><mo>⊥</mo></mrow></msup><mi>ψ</mi><mo>.</mo><mo>∇</mo><mi>Δ</mi><mi>ψ</mi><mo>+</mo><mi>β</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mi>ψ</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>H</mi></mrow></mfrac><msub><mrow><mrow><mo>(</mo><mo>∇</mo><mo>×</mo><mi>τ</mi><mo>)</mo></mrow></mrow><mrow><mi>v</mi></mrow></msub><mo>−</mo><mi>μ</mi><mi>Δ</mi><mi>ψ</mi><mo>+</mo><mi>ɛ</mi><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>ψ</mi><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>ψ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mi>τ</mi></math></span> are the streamfunction and the wind stress tensor, respectively. This equation encodes the <em>western boundary layer problem</em> (Ghil et al. 2008) for the potential vorticity <span><math><mi>ψ</mi></math></span>, which corresponds to the sharp contrast between the gyres flow in the oceanic circulation at mid-latitude and the strong western boundary currents. Numerical results for Equation (MK-1D) show that, with this two-scale scheme, high order accuracy is preserved for <span><math><mi>u</mi></math></span> and <span><math><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac></mrow><mo>)</mo></mrow><mi>u</mi></mrow></math></span> both in the boundary layer and in the central zone of the domain. The test cases are taken from Chekroun et al. 2020.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"466 ","pages":"Article 116595"},"PeriodicalIF":2.1,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551036","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}