Pub Date : 2025-10-01DOI: 10.1016/j.aml.2025.109780
Yawen Mao , Chen Xu , Jiahe Yu , Feng Ding
This letter proposes a multiple-direction conjugate gradient (MD-CG) iterative algorithm accelerated by Gram–Schmidt -orthogonalization for parameter estimation in nonlinear NARMAX systems. Unlike the traditional CG algorithm that updates along a single conjugate direction per iteration, the MD-CG algorithm generates mutually -orthogonal search directions through a modified Gram–Schmidt process, and the convergence speed increases with increasing . Theoretical analysis shows that the convergence speed of the MD-CG algorithm can reach th power acceleration of the CG algorithm under ideal conditions, and is especially suitable for large-scale systems. A simulation example is provided to verify the superiority of the proposed algorithm in terms of parameter estimation speed and accuracy.
本文提出了一种由Gram-Schmidt a -正交化加速的多方向共轭梯度（MD-CG）迭代算法，用于非线性NARMAX系统的参数估计。与传统CG算法每次迭代沿单一共轭方向更新不同，MD-CG算法通过改进的Gram-Schmidt过程生成p个相互a正交的搜索方向，并且收敛速度随着p的增加而增加。理论分析表明，MD-CG算法的收敛速度在理想条件下可以达到CG算法的p次幂加速度，特别适用于大型系统。仿真实例验证了该算法在参数估计速度和精度方面的优越性。
{"title":"Multiple-direction conjugate gradient method via Gram–Schmidt A-orthogonalization with applications to nonlinear system identification","authors":"Yawen Mao , Chen Xu , Jiahe Yu , Feng Ding","doi":"10.1016/j.aml.2025.109780","DOIUrl":"10.1016/j.aml.2025.109780","url":null,"abstract":"<div><div>This letter proposes a multiple-direction conjugate gradient (MD-CG) iterative algorithm accelerated by Gram–Schmidt <span><math><mi>A</mi></math></span>-orthogonalization for parameter estimation in nonlinear NARMAX systems. Unlike the traditional CG algorithm that updates along a single conjugate direction per iteration, the MD-CG algorithm generates <span><math><mi>p</mi></math></span> mutually <span><math><mi>A</mi></math></span>-orthogonal search directions through a modified Gram–Schmidt process, and the convergence speed increases with increasing <span><math><mi>p</mi></math></span>. Theoretical analysis shows that the convergence speed of the MD-CG algorithm can reach <span><math><mi>p</mi></math></span>th power acceleration of the CG algorithm under ideal conditions, and is especially suitable for large-scale systems. A simulation example is provided to verify the superiority of the proposed algorithm in terms of parameter estimation speed and accuracy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109780"},"PeriodicalIF":2.8,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268033","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}
Pub Date : 2025-09-30DOI: 10.1016/j.aml.2025.109776
Di Lei, Huiyan Li, Jing Niu
This paper focuses on proving the stability of the Runge–Kutta spectral volume (RKSV) scheme for solving one-dimensional equations, with a specific analysis of the Radau spectral volume (RRSV) and Gauss–Legendre spectral volume (LSV) schemes. By comparing the similarities and discrepancies between the Runge–Kutta spectral volume (RKSV) and Runge–Kutta discontinuous Galerkin (RKDG) schemes, we transform the stability analysis of the RKSV scheme into that of the RKDG scheme-an approach that already possesses a well-established theoretical analysis basis. Our key findings reveal two critical results: first, the Runge–Kutta Radau spectral volume (RKRRSV) scheme is entirely equivalent to the RKDG scheme; second, under the framework of a newly defined norm, the Runge–Kutta Gauss–Legendre spectral volume (RKLSV) scheme yields stability results identical to those of the RKDG scheme. Furthermore, numerical experiments are conducted to validate both the stability and optimal convergence properties of the RKSV scheme, providing empirical support for its theoretical conclusions.
{"title":"The stability of Runge–Kutta spectral volume methods for 1-D linear hyperbolic equations with constant coefficients","authors":"Di Lei, Huiyan Li, Jing Niu","doi":"10.1016/j.aml.2025.109776","DOIUrl":"10.1016/j.aml.2025.109776","url":null,"abstract":"<div><div>This paper focuses on proving the stability of the Runge–Kutta spectral volume (RKSV) scheme for solving one-dimensional equations, with a specific analysis of the Radau spectral volume (RRSV) and Gauss–Legendre spectral volume (LSV) schemes. By comparing the similarities and discrepancies between the Runge–Kutta spectral volume (RKSV) and Runge–Kutta discontinuous Galerkin (RKDG) schemes, we transform the stability analysis of the RKSV scheme into that of the RKDG scheme-an approach that already possesses a well-established theoretical analysis basis. Our key findings reveal two critical results: first, the Runge–Kutta Radau spectral volume (RKRRSV) scheme is entirely equivalent to the RKDG scheme; second, under the framework of a newly defined norm, the Runge–Kutta Gauss–Legendre spectral volume (RKLSV) scheme yields stability results identical to those of the RKDG scheme. Furthermore, numerical experiments are conducted to validate both the stability and optimal convergence properties of the RKSV scheme, providing empirical support for its theoretical conclusions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109776"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220890","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}
Pub Date : 2025-09-30DOI: 10.1016/j.aml.2025.109777
Xi-Hu Wu , Run-Fa Zhang
Spin waves, as charge-free collective excitations of electron spins, are fundamental to the development of energy-efficient spintronic devices and wave-based computing. This Letter investigates a higher-order Heisenberg ferromagnetic model characterizing the dynamics of the magnetic vector in isotropic ferromagnetism. We construct a direct -fold Darboux transformation (DT) and a generalized -fold DT in the compact determinant forms, which enhance the efficiency of obtaining rogue wave, multiple, multi-pole and mixed solutions for the nonlinear systems within the Heisenberg ferromagnetic hierarchy. Those results also help provide a mathematical framework for exploring complex spin wave interactions in ferromagnetic materials.
{"title":"Compact Darboux transformation and multi-pole magnetic waves within a higher-order Heisenberg ferromagnetic model","authors":"Xi-Hu Wu , Run-Fa Zhang","doi":"10.1016/j.aml.2025.109777","DOIUrl":"10.1016/j.aml.2025.109777","url":null,"abstract":"<div><div>Spin waves, as charge-free collective excitations of electron spins, are fundamental to the development of energy-efficient spintronic devices and wave-based computing. This Letter investigates a higher-order Heisenberg ferromagnetic model characterizing the dynamics of the magnetic vector in isotropic ferromagnetism. We construct a direct <span><math><mi>N</mi></math></span>-fold Darboux transformation (DT) and a generalized <span><math><mi>N</mi></math></span>-fold DT in the compact determinant forms, which enhance the efficiency of obtaining rogue wave, multiple, multi-pole and mixed solutions for the nonlinear systems within the Heisenberg ferromagnetic hierarchy. Those results also help provide a mathematical framework for exploring complex spin wave interactions in ferromagnetic materials.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109777"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220889","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}
Pub Date : 2025-09-30DOI: 10.1016/j.aml.2025.109775
Xin Zhang , Lin Li , Jijiang Sun
In this paper, we study the following degenerate Kirchhoff-type problem where is a bounded smooth domain, are constants, and . Using genus theory, symmetric mountain pass lemma and cut-off technique, we prove the existence of infinitely many solutions for an odd nonlinearity . Depending on whether is superlinear or sublinear at the origin, we show that the corresponding solution sequence either has energies concentrating at the critical level or converges to zero in the norm.
{"title":"Multiplicity and asymptotic behavior of solutions for a degenerate Kirchhoff type problem","authors":"Xin Zhang , Lin Li , Jijiang Sun","doi":"10.1016/j.aml.2025.109775","DOIUrl":"10.1016/j.aml.2025.109775","url":null,"abstract":"<div><div>In this paper, we study the following degenerate Kirchhoff-type problem <span><span><span><math><mfenced><mrow><mtable><mtr><mtd></mtd><mtd><mo>−</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mrow><mo>(</mo><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> is a bounded smooth domain, <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></mrow></math></span> are constants, and <span><math><mrow><mi>f</mi><mo>∈</mo><mi>C</mi><mrow><mo>(</mo><mi>Ω</mi><mo>×</mo><mi>R</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>. Using genus theory, symmetric mountain pass lemma and cut-off technique, we prove the existence of infinitely many solutions for an odd nonlinearity <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span>. Depending on whether <span><math><mi>f</mi></math></span> is superlinear or sublinear at the origin, we show that the corresponding solution sequence either has energies concentrating at the critical level <span><math><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mrow><mo>(</mo><mn>4</mn><mi>b</mi><mo>)</mo></mrow></mrow></math></span> or converges to zero in the <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> norm.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109775"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268034","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}
Pub Date : 2025-09-30DOI: 10.1016/j.aml.2025.109778
Rui Wang , Juntao Sun , Sofiane Khoutir , Han-Su Zhang
In this paper, we are concerned with the multiplicity of normalized solutions for a class of Kirchhoff equations with the nonlinearity in , where and . We explore the relationship between the number of solutions and the shape of the weight function .
{"title":"Multiple normalized solutions for non-autonomous Kirchhoff equations with mass-subcritical nonlinearity in R3","authors":"Rui Wang , Juntao Sun , Sofiane Khoutir , Han-Su Zhang","doi":"10.1016/j.aml.2025.109778","DOIUrl":"10.1016/j.aml.2025.109778","url":null,"abstract":"<div><div>In this paper, we are concerned with the multiplicity of normalized solutions for a class of Kirchhoff equations with the nonlinearity <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mi>ɛ</mi><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where <span><math><mrow><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mn>4</mn><mo>≤</mo><mi>p</mi><mo><</mo><mn>14</mn><mo>/</mo><mn>3</mn></mrow></math></span>. We explore the relationship between the number of solutions and the shape of the weight function <span><math><mi>h</mi></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109778"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220885","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}
Pub Date : 2025-09-29DOI: 10.1016/j.aml.2025.109772
Dongxue Yan , Xinyu Bai , Yu Cao
Using semigroup theories and spectral analysis methods, this paper shows that the solutions of a Daphnia population model with size structure and delayed birth process exhibit asynchronous exponential growth under some conditions.
{"title":"Asynchronous exponential growth for a size-structured population model of Daphnia with delayed birth process","authors":"Dongxue Yan , Xinyu Bai , Yu Cao","doi":"10.1016/j.aml.2025.109772","DOIUrl":"10.1016/j.aml.2025.109772","url":null,"abstract":"<div><div>Using semigroup theories and spectral analysis methods, this paper shows that the solutions of a Daphnia population model with size structure and delayed birth process exhibit asynchronous exponential growth under some conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109772"},"PeriodicalIF":2.8,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220887","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}
Pub Date : 2025-09-29DOI: 10.1016/j.aml.2025.109774
Na Wang , Sébastien Boyaval , Yuxi Hu
We prove finite-time blowup of classical solutions for the compressible Upper Convective Maxwell (UCM) viscoelastic fluid system. By establishing a key energy identity and adapting Sideris’ method for compressible flows, we derive a Riccati-type inequality for a momentum functional. For initial data with compactly supported perturbations satisfying a sufficiently large condition, all classical solutions lose regularity in finite time. This constitutes the first rigorous blowup result for multidimensional compressible viscoelastic fluids.
{"title":"Blowup of solutions for compressible viscoelastic fluid","authors":"Na Wang , Sébastien Boyaval , Yuxi Hu","doi":"10.1016/j.aml.2025.109774","DOIUrl":"10.1016/j.aml.2025.109774","url":null,"abstract":"<div><div>We prove finite-time blowup of classical solutions for the compressible Upper Convective Maxwell (UCM) viscoelastic fluid system. By establishing a key energy identity and adapting Sideris’ method for compressible flows, we derive a Riccati-type inequality for a momentum functional. For initial data with compactly supported perturbations satisfying a sufficiently large condition, all classical solutions lose regularity in finite time. This constitutes the first rigorous blowup result for multidimensional compressible viscoelastic fluids.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109774"},"PeriodicalIF":2.8,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220996","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}
A model order reduction method based on shifted Legendre polynomials for solving convection–diffusion equations with variable coefficients is presented in this paper. The ordinary differential system of the convection–diffusion equation is obtained by finite element discretization procedure. Then, approximating the system state via shifted Legendre polynomials, the reduced-order system is produced, which can be solved efficiently to obtain the numerical solution. Error analysis is presented, and numerical examples are used to verify the feasibility of the presented method.
{"title":"Legendre-based model order reduction method for solving convection–diffusion equations with variable coefficients","authors":"Zhiyuan Xing , Yanpeng Li , Xiufang Feng , Yaolin Jiang","doi":"10.1016/j.aml.2025.109773","DOIUrl":"10.1016/j.aml.2025.109773","url":null,"abstract":"<div><div>A model order reduction method based on shifted Legendre polynomials for solving convection–diffusion equations with variable coefficients is presented in this paper. The ordinary differential system of the convection–diffusion equation is obtained by finite element discretization procedure. Then, approximating the system state via shifted Legendre polynomials, the reduced-order system is produced, which can be solved efficiently to obtain the numerical solution. Error analysis is presented, and numerical examples are used to verify the feasibility of the presented method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109773"},"PeriodicalIF":2.8,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220888","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}
Pub Date : 2025-09-27DOI: 10.1016/j.aml.2025.109771
Hongjie Fan , Kai Wang , Yanling Zhu
In this paper, we propose and investigate a stochastic SEQIR epidemic model with Markovian regime-switching. Governmental policies and their implementation efficiency are incorporated by a generalized incidence function of the susceptible class. Using the Lyapunov method, we illustrate the existence and uniqueness of the globally positive solution to the stochastic model. Furthermore, we also analyze the dynamical behaviors of the disease, and derive sufficient conditions for its extinction and persistence in mean. Finally, numerical simulations are presented to verify the theoretical findings.
{"title":"Dynamics analysis of a stochastic regime-switching transmission model with governmental policy","authors":"Hongjie Fan , Kai Wang , Yanling Zhu","doi":"10.1016/j.aml.2025.109771","DOIUrl":"10.1016/j.aml.2025.109771","url":null,"abstract":"<div><div>In this paper, we propose and investigate a stochastic SEQIR epidemic model with Markovian regime-switching. Governmental policies and their implementation efficiency are incorporated by a generalized incidence function of the susceptible class. Using the Lyapunov method, we illustrate the existence and uniqueness of the globally positive solution to the stochastic model. Furthermore, we also analyze the dynamical behaviors of the disease, and derive sufficient conditions for its extinction and persistence in mean. Finally, numerical simulations are presented to verify the theoretical findings.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109771"},"PeriodicalIF":2.8,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220886","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}
Pub Date : 2025-09-25DOI: 10.1016/j.aml.2025.109770
Sheng Liu, Xi-Le Zhao, Qin Jiang
The tensor-tensor product (t-product) is a fundamental operation in tensor decomposition, enabling effective modeling of interactions between third-order tensors. However, the classical t-product is restricted by the fact that the two factors must have the same third-mode dimension, limiting its flexibility and expressiveness. To break this restriction, we introduce an inconsistent tensor-tensor product (it-product), which allows tensors with inconsistent third-mode dimensions to interact with each other while still respecting the algebraic structure of classical t-product. Equipped with the proposed it-product, we develop an it-product-based low-rank tensor factorization and suggest a unified model for tensor completion and tensor compression. To address the resulting nonconvex optimization problem, we build a proximal alternating minimization (PAM)-based algorithm. We further provide a theoretical convergence analysis, showing that the sequence generated by the algorithm converges to a critical point of the objective function under certain conditions. Numerical experiments on real-world datasets have been conducted to validate the effectiveness and superiority of the proposed method over existing baselines.
{"title":"Inconsistent tensor-tensor product for low-rank tensor factorization","authors":"Sheng Liu, Xi-Le Zhao, Qin Jiang","doi":"10.1016/j.aml.2025.109770","DOIUrl":"10.1016/j.aml.2025.109770","url":null,"abstract":"<div><div>The tensor-tensor product (t-product) is a fundamental operation in tensor decomposition, enabling effective modeling of interactions between third-order tensors. However, the classical t-product is restricted by the fact that the two factors must have the same third-mode dimension, limiting its flexibility and expressiveness. To break this restriction, we introduce an inconsistent tensor-tensor product (it-product), which allows tensors with inconsistent third-mode dimensions to interact with each other while still respecting the algebraic structure of classical t-product. Equipped with the proposed it-product, we develop an it-product-based low-rank tensor factorization and suggest a unified model for tensor completion and tensor compression. To address the resulting nonconvex optimization problem, we build a proximal alternating minimization (PAM)-based algorithm. We further provide a theoretical convergence analysis, showing that the sequence generated by the algorithm converges to a critical point of the objective function under certain conditions. Numerical experiments on real-world datasets have been conducted to validate the effectiveness and superiority of the proposed method over existing baselines.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109770"},"PeriodicalIF":2.8,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158602","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}
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