Journal of Computational and Applied Mathematics最新文献

{"title":"A new extension of the core inverse","authors":"D. Mosić ,&nbsp;D.E. Ferreyra","doi":"10.1016/j.cam.2024.116305","DOIUrl":"10.1016/j.cam.2024.116305","url":null,"abstract":"<div><div>There are a number of extensions of the core inverse represented by the products of known generalized inverses, like the core-EP inverse, DMP inverse, GC inverse and so on. However, none of them is an inner inverse of the matrix, and especially for an arbitrary nilpotent matrix, such inverses are always null. Our goal is to use a new technic to introduce an extension of the core inverse that preserves the interesting property of being an inner inverse of the matrix which need not necessarily be the null matrix of a nilpotent matrix. We define the extended core inverse for square complex matrices combining the sum and the difference of three known generalized inverses. Various properties and representations of the extended core inverse are developed. The extended dual core inverse is investigated too. We apply the extended core inverse to solve some systems of linear equations and one minimization problem. A significant normal equation related to least-squares solutions can be solved using the extended core inverse.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433435","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":"Optimal L2 error estimates of mass- and energy- conserved FE schemes for a nonlinear Schrödinger–type system","authors":"Zhuoyue Zhang,&nbsp;Wentao Cai","doi":"10.1016/j.cam.2024.116313","DOIUrl":"10.1016/j.cam.2024.116313","url":null,"abstract":"<div><div>In this paper, we present an implicit Crank–Nicolson finite element (FE) scheme for solving a nonlinear Schrödinger–type system, which includes Schrödinger–Helmholz system and Schrödinger–Poisson system. In our numerical scheme, we employ an implicit Crank–Nicolson method for time discretization and a conforming FE method for spatial discretization. The proposed method is proved to be well-posedness and ensures mass and energy conservation at the discrete level. Furthermore, we prove optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> error estimates for the fully discrete solutions. Finally, some numerical examples are provided to verify the convergence rate and conservation properties.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437849","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":"Dispersion analysis of SPH for parabolic equations: High-order kernels against tensile instability","authors":"O.P. Stoyanovskaya ,&nbsp;O.A. Burmistrova ,&nbsp;M.S. Arendarenko ,&nbsp;T.V. Markelova","doi":"10.1016/j.cam.2024.116316","DOIUrl":"10.1016/j.cam.2024.116316","url":null,"abstract":"<div><div>The Smoothed Particle Hydrodynamics (SPH) is a meshless particle-based method mainly used to solve dynamical problems for partial differential equations (PDE). By means of dispersion analysis we investigated four classical SPH-discretizations of parabolic PDE differing by the approximation of Laplacian.</div><div>We derived approximate dispersion relations (ADR) for considered SPH-approximations of the Burgers equation. We demonstrated how the analysis of the ADR allows both studying the approximation and stability of numerical scheme and explaining the features of the method that are known from practice, but are counter-intuitive from the theoretical point of view.</div><div>By means of the mathematical analysis of ADR, the phenomenon of conditional approximation of some schemes under consideration is shown. Moreover, we pioneered in obtaining the necessary condition for the stability of the SPH-approximation of parabolic equations in terms of the Fredholm integral operator applied to the function defined by the kernel of the SPH method. Using this condition, we revealed that passing from the classical second-order kernels to high-order kernels for some schemes leads to the appearance of tensile (short-wave) instability. Among the schemes under consideration, we found the one, for which the necessary condition for the stability of short waves is satisfied both for classical and high-order kernels. The fourth order of approximation in space of this scheme is shown theoretically and confirmed in practice.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532045","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":"Error bounds for Gauss–Lobatto quadrature of analytic functions on an ellipse","authors":"Hiroshi Sugiura ,&nbsp;Takemitsu Hasegawa","doi":"10.1016/j.cam.2024.116326","DOIUrl":"10.1016/j.cam.2024.116326","url":null,"abstract":"&lt;div&gt;&lt;div&gt;For the (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;)-point Gauss–Jacobi–Lobatto quadrature to integrals with the Jacobi weight function &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;) over the interval &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, we estimate the location where the kernel of the error functional for functions analytic on an ellipse and its interior in the complex plane attains its maximum modulus. As in our previous work on the Gauss–Jacobi rule, when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, the location is the intersection point of the ellipse with the real axis in the complex plane. When &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; (the Gegenbauer weight), it is the intersection points with the real axis for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; or for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and with the imaginary axis for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; or for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Here, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;) is a monotonously decreasing function for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;lim&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Some nume","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445772","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 posteriori error estimates and adaptivity for the IMEX BDF2 method for nonlinear parabolic equations","authors":"Shuo Yang,&nbsp;Liutao Tian,&nbsp;Hongjiong Tian","doi":"10.1016/j.cam.2024.116318","DOIUrl":"10.1016/j.cam.2024.116318","url":null,"abstract":"<div><div>In this paper, we establish optimal a posteriori error estimates for time discretizations by the IMEX two-step backward differentiation formula (BDF2) method for nonlinear parabolic equations. An effective tool for such derivation is appropriate second-order reconstructions of the piecewise linear approximate solution. We employ the second-order reconstructions to establish the upper and lower error bounds which depend only on the data of the problem and the discretization parameters. By means of the a posteriori error estimates, we design a time adaptive algorithm of IMEX BDF2 method. Numerical experiments for the Allen–Cahn equation with smooth and non-smooth initial data are performed to verify our theoretical results and demonstrate the efficiency of the time adaptive algorithm. In addition, we use the IMEX BDF2 method to solve the Navier–Stokes equations to test the validity of the a posteriori error estimates.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441066","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":"Moreau-Yosida regularization to optimal control of the monodomain model with pointwise control and state constraints in cardiac electrophysiology","authors":"Maria Robert ,&nbsp;Suresh Kumar Nadupuri ,&nbsp;Nagaiah Chamakuri","doi":"10.1016/j.cam.2024.116306","DOIUrl":"10.1016/j.cam.2024.116306","url":null,"abstract":"<div><div>In this work, we study the optimal control problem of a coupled reaction-diffusion system, which is a monodomain model in cardiac electrophysiology with pointwise bilateral control and state constraints. We adopt the Moreau-Yosida regularization as a penalization technique to deal with the state constraints. The regularized problem’s first-order optimality condition is derived. In addition, sufficient second-order optimality condition is derived for the regularized problem using the virtual control concept by proving equivalence between Moreau-Yosida regularization and the virtual control concept. The convergence of optimal controls of the regularized problems to the optimal control of the original problem is proved. Moreover, the semi-smooth Newton method for numerically finding the optimal solution to the regularization problem is presented. Finally, numerical experiments are conducted, and the results allow us to understand the extinction of the wave excitation in cardiac defibrillation in the presence of both control and state constraints.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441064","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":"Population-based algorithm for discrete facility location with ranking of candidate locations","authors":"Algirdas Lančinskas ,&nbsp;Julius Žilinskas ,&nbsp;Pascual Fernández ,&nbsp;Blas Pelegrín","doi":"10.1016/j.cam.2024.116304","DOIUrl":"10.1016/j.cam.2024.116304","url":null,"abstract":"<div><div>Facility location problems are mathematical optimization problems that involve finding the best locations for facilities (e.g., factories, warehouses, stores) to serve customers within a given geographic area. The goal is typically to minimize costs, maximize efficiency, or optimize other objectives. Facility location problems can vary in several ways, including customer behavior rules, the type of search space, and constraints on locations for new facilities being located. These variations directly impact the complexity of the problem and the appropriate solution methods that can be used to tackle the problem. This research is focused on the discrete competitive facility location problem for an entering firm, which is a crucial scenario for new firms entering the existing market. The goal is to strategically locate new facilities to maximize their profit, while considering existing competitors. A new random search heuristic algorithm to approximate the optimal solution for discrete competitive facility location problems for firm expansion has been developed. The algorithm extends its precursor that ranks potential locations for the new facilities depending on their usefulness and uselessness in creating new solutions in the past. The new algorithm uses a population to handle and reuse the best solutions found so far and new strategies for ranking potential locations, considering features of the solutions in the population. The designed algorithm has been investigated by solving competitive facility location problems actual for an entering firms using real geographical data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426745","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 two-step relaxed-inertial derivative-free projection based algorithm for solving standard nonlinear pseudo-monotone equations and logistic regression problems","authors":"Wenli Liu ,&nbsp;Jinbao Jian ,&nbsp;Jianghua Yin","doi":"10.1016/j.cam.2024.116327","DOIUrl":"10.1016/j.cam.2024.116327","url":null,"abstract":"<div><div>This paper explores a two-step inertial derivative-free projection method with a relaxation factor <span><math><mrow><mi>γ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> for solving nonlinear pseudo-monotone equations. Unlike existing inertial algorithms for the system of nonlinear pseudo-monotone equations, the inertial step of our method involves the current iteration point and the previous two iteration points. In particular, one of the inertial parameters is nonpositive. In the proposed algorithm, the search direction possesses not only the sufficient descent property but also the trust region property, independent of the line search technique. Moreover, we also establish the global convergence and the convergence rate of the algorithm without the Lipschitz continuity of the underlying mapping. Finally, our method provides competitive results on standard nonlinear monotone and pseudo-monotone equations and logistic regression problems compared with two inertial algorithms existing in the literature.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531791","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":"Domain decomposition with local time discretization for the nonlinear Stokes–Biot system","authors":"Hemanta Kunwar ,&nbsp;Hyesuk Lee","doi":"10.1016/j.cam.2024.116311","DOIUrl":"10.1016/j.cam.2024.116311","url":null,"abstract":"<div><div>This work presents a domain decomposition method for the fluid-poroelastic structure interaction (FPSI) system, which utilizes local time integration for subproblems. To derive the domain decomposition scheme, we introduce a Lagrange multiplier and define time-dependent Steklov–Poincaré-type operators based on the interface conditions. These operators are employed to transform the coupled system into an evolutionary nonlinear interface problem, which is then solved using an iterative algorithm. This approach provides the flexibility to use different time discretization schemes and step sizes in subdomains, making it an efficient method for simulating multiphysics systems. We present numerical tests for both non-physical and physical problems to demonstrate the accuracy and efficiency of this method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445770","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":"On the causality-preservation capabilities of generative modelling","authors":"Yves-Cédric Bauwelinckx ,&nbsp;Jan Dhaene ,&nbsp;Milan van den Heuvel ,&nbsp;Tim Verdonck","doi":"10.1016/j.cam.2024.116312","DOIUrl":"10.1016/j.cam.2024.116312","url":null,"abstract":"<div><div>Modelling is essential in both the financial and insurance industries. The emergence of machine learning and deep learning models offers new tools for this, but they often require large datasets that are typically unavailable in business fields due to privacy and ethical concerns. This lack of data is currently one of the main hurdles in developing better models. Generative modelling, such as Generative Adversarial Networks (GANs), can address this issue by creating synthetic data that can be freely shared. While GANs are widely studied in fields like computer vision, their use in business is limited, primarily because business questions often focus on identifying causal effects, whereas GANs and neural networks typically emphasise high-dimensional correlations. This paper explores whether GANs can produce synthetic data that reliably answers causal questions by performing causal analyses on GAN-generated data under varying assumptions. The study includes cross-sectional, time series, and complete structural model scenarios. Findings show that while basic GANs replicate causal relationships in simple cross-sectional data, they struggle with more complex structural models. In contrast, CausalGAN effectively replicates the original causal model, and TimeGAN modifies the causal representation in time series data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445744","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}