Journal of Computational and Applied Mathematics最新文献

{"title":"Galois duality of matrix product codes with applications","authors":"Ramy Taki Eldin","doi":"10.1016/j.cam.2025.116954","DOIUrl":"10.1016/j.cam.2025.116954","url":null,"abstract":"<div><div>In recent literature, matrix product (MP) codes and their duals have gained significant attention due to their applications in constructing quantum stabilizer codes. In this paper, we present a general formula characterizing the Galois dual of MP codes. Using this formula, we establish necessary and sufficient conditions under which MP codes are Galois self-orthogonal and dual-containing. Unlike previous results that describe the Euclidean and Hermitian duals of MP codes only under specific assumptions on the defining matrix, our characterization applies to MP codes with defining matrices that are not necessarily square nor of full row rank. Moreover, we consider the more general framework of Galois duals, with Euclidean and Hermitian duals treated as special cases. To demonstrate the theoretical results, several numerical examples of MP codes with best-known parameters are provided.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116954"},"PeriodicalIF":2.6,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749293","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":"Neural networks for solving least squares solution of polynomial systems with time-varying tensors","authors":"Jianhua Li ,&nbsp;Xuezhong Wang ,&nbsp;Kai Wang ,&nbsp;Yimin Wei","doi":"10.1016/j.cam.2025.116952","DOIUrl":"10.1016/j.cam.2025.116952","url":null,"abstract":"<div><div>This study introduces a groundbreaking least squares approach tailored for solving time-varying tensor polynomial systems, where both coefficients and right-hand side vectors evolve dynamically over time. To address this challenge, we propose two innovative neural networks: HNN and MwsbpHNN.</div><div>HNN is designed to converge to a least squares solution of the time-varying tensor polynomial systems, demonstrating its efficacy in handling dynamic data. MwsbpHNN takes this a step further by achieving fixed-time convergence, a significant advancement over existing methods, while simultaneously exhibiting noise tolerance, ensuring robust performance even in noisy environments. We derive rigorous upper bounds on the convergence time for MwsbpHNN, providing a theoretical foundation for its rapid and reliable operation.</div><div>Numerical simulations validate the effectiveness and robustness of both HNN and MwsbpHNN, underscoring their potential to revolutionize the field of tensor polynomial system solving.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116952"},"PeriodicalIF":2.6,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757931","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 fast generalized prediction–correction dual–primal hybrid gradient algorithm for bilinear saddle point problems with applications to total variation image processing","authors":"Si Li ,&nbsp;Shibei Xue ,&nbsp;Lihan Zhou ,&nbsp;Shan Ma","doi":"10.1016/j.cam.2025.116956","DOIUrl":"10.1016/j.cam.2025.116956","url":null,"abstract":"<div><div>The primal–dual hybrid gradient (PDHG) algorithm has been extensively studied and utilized for solving bilinear saddle point problems due to its inexpensive computations. Most recently, a prediction–correction PDHG (PC-PDHG) algorithm has been proposed in literature for solving linearly constrained convex optimization problems, which improves the convergence condition of PDHG and accelerates its numerical performance. In this paper, we introduce a dual–primal version of the newly developed PC-PDHG algorithm and extend its applicability to general bilinear saddle point problems, resulting in the generalized new prediction–correction dual–primal hybrid gradient (GNPC-DPHG) algorithm. In many instances, the proposed algorithm significantly reduces the number of iterations compared to the original algorithm, while only adding a small amount of computational cost per iteration, thereby enhancing the convergence rate. Furthermore, we provide a rigorous proof of the global convergence of the proposed GNPC-DPHG algorithm. Finally, numerical experiments demonstrate that the proposed algorithm can achieve faster convergence compared to the original algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116956"},"PeriodicalIF":2.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757929","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 RBF-based Nyström method for Second–Kind Fredholm Integral Equations","authors":"Roberto Cavoretto ,&nbsp;Alessandra De Rossi ,&nbsp;Anna Lucia Laguardia ,&nbsp;Domenico Mezzanotte ,&nbsp;Donatella Occorsio ,&nbsp;Maria Grazia Russo","doi":"10.1016/j.cam.2025.116968","DOIUrl":"10.1016/j.cam.2025.116968","url":null,"abstract":"<div><div>The aim of this paper is to numerically solve Fredholm Integral Equations (FIEs) of the second kind, when the right-hand side term and the kernel are known only at scattered sample points. The proposed method is of the Nyström type and leverages a cubature rule based on Radial Basis Function (RBF) interpolation, with the Leave-One-Out Cross-Validation (LOOCV) technique used to select the optimal RBF shape parameter. The convergence of the method is proven in the space of continuous functions. Finally, numerical tests demonstrate the performance of the method for various RBF choices and provide direct comparisons with other RBF-based techniques for FIEs available in the literature.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116968"},"PeriodicalIF":2.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749294","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":"Data-driven discovery of state-changes in underlying system from hidden change-points in partial differential equations with spatiotemporal varying coefficients","authors":"Guangtao Zhang ,&nbsp;Yiting Duan ,&nbsp;Guanyu Pan ,&nbsp;Qijing Chen ,&nbsp;Huiyu Yang ,&nbsp;Zhikun Zhang","doi":"10.1016/j.cam.2025.116962","DOIUrl":"10.1016/j.cam.2025.116962","url":null,"abstract":"<div><div>To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity, making the solution of the parameter inverse problem from observed spatiotemporal data a challenging task. Starting from the observed data obtained from such systems, we propose a novel framework that facilitates the investigation of parameter identification for multi-state systems governed by spatiotemporal varying parametric partial differential equations. Our framework consists of two integral components: a constrained self-adaptive physics-informed neural networks, encompassing a sub-network, and a finite mixture model with Gaussian components, as our methodology for parameter identification and change-point detection. Through our scheme, we can accurately estimate the unknown varying parameters of the complex multi-state system. Furthermore, we have showcased the efficacy of our framework on two numerical cases: the 1D Burgers’ equation with time-varying parameters and the 2D wave equation with a space-varying parameter.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116962"},"PeriodicalIF":2.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748546","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":"Generalized co-polynomials of RII type and associated quadrature rules","authors":"Vinay Shukla ,&nbsp;A. Swaminathan","doi":"10.1016/j.cam.2025.116957","DOIUrl":"10.1016/j.cam.2025.116957","url":null,"abstract":"<div><div>When the co-recursion and co-dilation in the recurrence relation of certain sequences of orthogonal polynomials are not at the same level, the behavior of the modified orthogonal polynomials is expected to have different properties compared to the situation of the same level of perturbation. This manuscript attempts to derive structural relations between the perturbed and original <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>I</mi><mi>I</mi></mrow></msub></math></span> type orthogonal polynomials. The classical result is improved using a transfer matrix approach. It turns out that the <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>I</mi><mi>I</mi></mrow></msub></math></span> fraction with perturbation is the rational spectral transformation of the unperturbed one. The derived notions are used to deduce some consequences for the polynomials orthogonal on the real line. A natural question that arises while dealing with perturbations at different levels, i.e., which perturbation, co-recursion or co-dilation, needs to be performed first, is answered.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116957"},"PeriodicalIF":2.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748545","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":"Equivalence of structured and unstructured pseudospectra for some doubly-structured matrices","authors":"Yang Yu,&nbsp;Guolin Hou","doi":"10.1016/j.cam.2025.116961","DOIUrl":"10.1016/j.cam.2025.116961","url":null,"abstract":"<div><div>In this paper, we give the affirmative answers to open problems about structured pseudospectra, proposed by R. Ferro and J. A. Virtanen in [<em>J. Comput. Appl. Math.</em> 322 (2017) 18-24]. Our primary contribution establishes the equivalence between the structured pseudospectra and unstructured pseudospectra for double-structured persymmetric Hankel and symmetric Toeplitz matrices in the complex case. Furthermore, we extend our analysis to analogous problems for centrosymmetric, Hermitian, skew-Hermitian, and circulant double-structured block matrices. The double structures are that the blocks of the given matrix are the same structure as the block matrix.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116961"},"PeriodicalIF":2.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749295","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":"Simplified Newton method for solving large-scale stochastic nonlinear matrix equations in mean-field social control","authors":"Zihang Tian,&nbsp;Hiroaki Mukaidani","doi":"10.1016/j.cam.2025.116935","DOIUrl":"10.1016/j.cam.2025.116935","url":null,"abstract":"<div><div>This paper investigates a numerical framework for solving incentive Stackelberg games in mean-field stochastic systems characterized by large numbers of followers. A well-known challenge in such systems is the computational bottleneck that arises as the follower count <span><math><mi>N</mi></math></span> approaches infinity, rendering implementation infeasible owing to exceeding physical limits. To address this issue, we propose a novel numerical algorithm that generates a decentralized Pareto strategy independent of the number of followers. Specifically, we developed a low-dimensional algorithm based on a simplified Newton’s method. This approach effectively handles the state dimension <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></math></span> of each follower by partitioning the very large-scale stochastic nonlinear matrix equations (SNMEs), which would otherwise require extensive computations in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mrow><mo>(</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>n</mi><mo>×</mo><mrow><mo>(</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>n</mi></mrow></msup></math></span> dimensions. We provide, for the first time, proof demonstrating the linear convergence of this method. Additionally, a Lyapunov iterative method is explored as an alternative to circumvent complex mathematical derivations. The proposed methods significantly reduce computational complexity by enabling low-dimensional computations for each follower, contrasting with the high-dimensional computations required by previous approaches. To prevent divergence of the norm of the solution, even with a small number of followers, we introduce a new condition for the coefficient matrices of the original mean-field stochastic system and develop an incentive strategy to ensure a finite norm. Finally, we validate the effectiveness and reliability of our algorithm by solving a large-scale set of SNMEs and confirming the linear convergence of the simplified Newton’s method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116935"},"PeriodicalIF":2.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757930","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":"Rational motions of minimal quaternionic degree with prescribed plane trajectories","authors":"Zülal Derin Yaqub,&nbsp;Hans-Peter Schröcker","doi":"10.1016/j.cam.2025.116949","DOIUrl":"10.1016/j.cam.2025.116949","url":null,"abstract":"<div><div>This paper investigates the construction of rational motions of a minimal quaternionic degree that generate a prescribed plane trajectory (a “rational torse”). Using the algebraic framework of dual quaternions, we formulate the problem as a system of polynomial equations. We derive necessary and sufficient conditions for the existence of such motions, establish a method to compute solutions and characterize solutions of minimal degree. Our findings reveal that a rational torse is realizable as a trajectory of a rational motion if and only if its Gauss map is rational. Furthermore, we demonstrate that the minimal degree of a motion polynomial is geometrically related to a drop of degree of the Gauss and algebraically determined by the structure of the torse’s associated plane polynomial and the real greatest common divisor of its vector part. The developed theoretical framework has potential applications in robotics, computer-aided design, and computational kinematic, offering a systematic approach to constructing rational motions of small algebraic complexity.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116949"},"PeriodicalIF":2.6,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723143","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":"Characterization of polynomial surfaces of revolution and polynomial quadrics","authors":"Michal Bizzarri ,&nbsp;Miroslav Lávička ,&nbsp;J. Rafael Sendra ,&nbsp;Jan Vršek","doi":"10.1016/j.cam.2025.116939","DOIUrl":"10.1016/j.cam.2025.116939","url":null,"abstract":"<div><div>In this paper, we characterize the polynomiality of surfaces of revolution by means of the polynomiality of an associated plane curve. In addition, if the surface of revolution is polynomial, we provide formulas for computing a polynomial parametrization, over <span><math><mi>ℂ</mi></math></span>, of the surface. Furthermore, we perform the first steps towards the analysis of the existence, and actual computation, of real polynomial parametrizations of surfaces of revolution. As a consequence, we give a complete picture of the real polynomiality of quadrics and we formulate a necessary condition for the general case.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116939"},"PeriodicalIF":2.6,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144739303","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}