Pub Date : 2026-09-01Epub Date: 2026-01-20DOI: 10.1016/j.cam.2026.117374
Bohdan Datsko , Vasyl Gafiychuk
Different types of instability and resulting pattern formation in a two-component incommensurate fractional reaction-diffusion system are studied. Considered system sets the possibility of continuous transitions between classical systems with integer derivatives. As a result, the presented investigations provide a better understanding of the instability conditions and nonlinear solutions not only in systems with fractional-order derivatives but also in classical two-component elliptic, parabolic, and hyperbolic systems, as well as those of a mixed type. Based on the linear stability analysis, the computer simulation of nonlinear dynamics in the fractional two-component system with cubic-like nonlinearity has been performed, demonstrating the rich diversity of pattern formation phenomena.
{"title":"Instabilities and pattern formation in fractional incommensurate activator-inhibitor reaction-diffusion systems","authors":"Bohdan Datsko , Vasyl Gafiychuk","doi":"10.1016/j.cam.2026.117374","DOIUrl":"10.1016/j.cam.2026.117374","url":null,"abstract":"<div><div>Different types of instability and resulting pattern formation in a two-component incommensurate fractional reaction-diffusion system are studied. Considered system sets the possibility of continuous transitions between classical systems with integer derivatives. As a result, the presented investigations provide a better understanding of the instability conditions and nonlinear solutions not only in systems with fractional-order derivatives but also in classical two-component elliptic, parabolic, and hyperbolic systems, as well as those of a mixed type. Based on the linear stability analysis, the computer simulation of nonlinear dynamics in the fractional two-component system with cubic-like nonlinearity has been performed, demonstrating the rich diversity of pattern formation phenomena.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117374"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039577","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 : 2026-09-01Epub Date: 2026-01-18DOI: 10.1016/j.cam.2026.117367
Paweł Przybyłowicz, Michał Sobieraj
In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the discretization parameter n and the size M of the random sample drawn at each step of the algorithm, in different subclasses of coefficients of the underlying SDE presenting various rates of convergence. Integral-form drift often appears when analyzing stochastic dynamics of optimization procedures in machine learning (ML) problems. Hence, we additionally discuss connections of the defined randomized Euler approximation scheme with the perturbed version of the stochastic gradient descent (SGD) algorithm. Finally, the results of numerical experiments performed using GPU architecture are also reported, including a comparison with other popular optimizers used in ML.
{"title":"On the randomized Euler scheme for stochastic differential equations with integral-form drift","authors":"Paweł Przybyłowicz, Michał Sobieraj","doi":"10.1016/j.cam.2026.117367","DOIUrl":"10.1016/j.cam.2026.117367","url":null,"abstract":"<div><div>In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the discretization parameter <em>n</em> and the size <em>M</em> of the random sample drawn at each step of the algorithm, in different subclasses of coefficients of the underlying SDE presenting various rates of convergence. Integral-form drift often appears when analyzing stochastic dynamics of optimization procedures in machine learning (ML) problems. Hence, we additionally discuss connections of the defined randomized Euler approximation scheme with the perturbed version of the stochastic gradient descent (SGD) algorithm. Finally, the results of numerical experiments performed using GPU architecture are also reported, including a comparison with other popular optimizers used in ML.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"483 ","pages":"Article 117367"},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039582","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 : 2026-08-15Epub Date: 2026-01-03DOI: 10.1016/j.cam.2026.117340
Fuad Kittaneh , Arnab Patra , Jyoti Rani
This study utilizes Orlicz functions to provide refined lower and upper bounds on the q-numerical radius of an operator acting on a Hilbert space. Additionally, the concept of q-sectorial matrices is introduced and further bounds for the q-numerical radius are established. Our results unify several existing bounds for the q-numerical radius. Suitable examples are provided to supplement the estimations.
{"title":"On the estimation of the q-numerical radius via Orlicz functions","authors":"Fuad Kittaneh , Arnab Patra , Jyoti Rani","doi":"10.1016/j.cam.2026.117340","DOIUrl":"10.1016/j.cam.2026.117340","url":null,"abstract":"<div><div>This study utilizes Orlicz functions to provide refined lower and upper bounds on the <em>q</em>-numerical radius of an operator acting on a Hilbert space. Additionally, the concept of <em>q</em>-sectorial matrices is introduced and further bounds for the <em>q</em>-numerical radius are established. Our results unify several existing bounds for the <em>q</em>-numerical radius. Suitable examples are provided to supplement the estimations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117340"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928325","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}
Large-scale quaternion matrix equations face challenges such as high dimensionality and non-commutativity of quaternion multiplication, which often result in high computational complexity and low efficiency with conventional methods. To this end, utilizing generalized Hamilton-real (GHR) calculus, we propose a quaternion random reshuffling (QRR) algorithm for solving large-scale quaternion matrix equations. We also provide a convergence analysis for the QRR algorithm. Numerical experiments show that the QRR algorithm achieves stable convergence performance and faster convergence rates in solving large-scale generalized Sylvester quaternion matrix equations. Thus, the QRR algorithm is expected to provide an efficient and robust solution for solving large-scale quaternion matrix equations.
{"title":"A random reshuffling method for generalized Sylvester quaternion matrix equations","authors":"Qiankun Diao , Yiming Jiang , Jinlan Liu , Dongpo Xu","doi":"10.1016/j.cam.2026.117346","DOIUrl":"10.1016/j.cam.2026.117346","url":null,"abstract":"<div><div>Large-scale quaternion matrix equations face challenges such as high dimensionality and non-commutativity of quaternion multiplication, which often result in high computational complexity and low efficiency with conventional methods. To this end, utilizing generalized Hamilton-real (GHR) calculus, we propose a quaternion random reshuffling (QRR) algorithm for solving large-scale quaternion matrix equations. We also provide a convergence analysis for the QRR algorithm. Numerical experiments show that the QRR algorithm achieves stable convergence performance and faster convergence rates in solving large-scale generalized Sylvester quaternion matrix equations. Thus, the QRR algorithm is expected to provide an efficient and robust solution for solving large-scale quaternion matrix equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117346"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979372","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 : 2026-08-15Epub Date: 2026-01-03DOI: 10.1016/j.cam.2026.117336
Dijana Mosić , Bibekananda Sitha
The fact that weak MPCEP and *CEPMP inverses of square matrices are generalizations of several classes of generalized inverses, inspired us to extend these concepts for rectangular matrices. Precisely, solvability of novel systems of equations is verified based on minimal rank W-weighted (right) weak Drazin inverse. As solutions of new extended systems, definitions of weighted weak MPCEP and *CEPMP inverses are presented, and some known weighted generalized inverses are unified. Characterizations and expressions for weighted weak MPCEP and *CEPMP inverses are given. Dual types of weighted weak MPCEP and *CEPMP inverses are studied too. As consequences, we get definitions and properties of dual weak MPCEP and *CEPMP inverses. Certain systems of linear equations are solved by applying weighted systems of linear equations.
{"title":"Weighted weak MPCEP and *CEPMP inverses","authors":"Dijana Mosić , Bibekananda Sitha","doi":"10.1016/j.cam.2026.117336","DOIUrl":"10.1016/j.cam.2026.117336","url":null,"abstract":"<div><div>The fact that weak MPCEP and *CEPMP inverses of square matrices are generalizations of several classes of generalized inverses, inspired us to extend these concepts for rectangular matrices. Precisely, solvability of novel systems of equations is verified based on minimal rank <em>W</em>-weighted (right) weak Drazin inverse. As solutions of new extended systems, definitions of weighted weak MPCEP and *CEPMP inverses are presented, and some known weighted generalized inverses are unified. Characterizations and expressions for weighted weak MPCEP and *CEPMP inverses are given. Dual types of weighted weak MPCEP and *CEPMP inverses are studied too. As consequences, we get definitions and properties of dual weak MPCEP and *CEPMP inverses. Certain systems of linear equations are solved by applying weighted systems of linear equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117336"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979370","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 : 2026-08-15Epub Date: 2025-12-26DOI: 10.1016/j.cam.2025.117313
Türkan Yeliz Gökc̣er Ellidokuz
In this paper, we present the nonlinear approximation operator using max-product operators of the combined Shepard operators constructed with Bernoulli polynomials.The linear counterpart known as the Shepard-Bernoulli operators is studied by Caira and Dell’accio (2006) in [10]. Compared to the Shepard-Bernoulli interpolation operators, we improve the approximation results using these nonlinear operators. Additionally, we generalize the approximation by applying the regular summability methods. To confirm the theory, we provide some applications and graphical representations.
{"title":"Approximation with max-product Shepard-Bernoulli operators","authors":"Türkan Yeliz Gökc̣er Ellidokuz","doi":"10.1016/j.cam.2025.117313","DOIUrl":"10.1016/j.cam.2025.117313","url":null,"abstract":"<div><div>In this paper, we present the nonlinear approximation operator using max-product operators of the combined Shepard operators constructed with Bernoulli polynomials.The linear counterpart known as the Shepard-Bernoulli operators is studied by Caira and Dell’accio (2006) in [10]. Compared to the Shepard-Bernoulli interpolation operators, we improve the approximation results using these nonlinear operators. Additionally, we generalize the approximation by applying the regular summability methods. To confirm the theory, we provide some applications and graphical representations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117313"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928324","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 : 2026-08-15Epub Date: 2025-12-28DOI: 10.1016/j.cam.2025.117257
Grigory Panasenko, Konstantin Pileckas
The stationary and non-stationary Navier-Stokes equations in a thin tube structure, with no slip boundary condition, are considered. A new method of partial asymptotic dimension reduction is introduced and justified by an error estimate. This method reduces the problem to a one-dimensional equation on the graph and several decoupled full dimension problems in small domains. The full dimension problems are independent and can be solved by parallel computing.
{"title":"Hybrid dimension modeling for Navier-Stokes equations in thin tube structures","authors":"Grigory Panasenko, Konstantin Pileckas","doi":"10.1016/j.cam.2025.117257","DOIUrl":"10.1016/j.cam.2025.117257","url":null,"abstract":"<div><div>The stationary and non-stationary Navier-Stokes equations in a thin tube structure, with no slip boundary condition, are considered. A new method of partial asymptotic dimension reduction is introduced and justified by an error estimate. This method reduces the problem to a one-dimensional equation on the graph and several decoupled full dimension problems in small domains. The full dimension problems are independent and can be solved by parallel computing.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117257"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928328","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 : 2026-08-15Epub Date: 2026-01-08DOI: 10.1016/j.cam.2026.117345
Jiamin Lu, Liwen Xu, Hao Cheng
In this paper, we investigate an inverse random source problem for the fractional pseudo-parabolic equation, where the source is driven by a fractional Brownian motion (fBm). For the direct problem, we illustrate the existence and uniqueness of the mild solution. For the inverse random source problem, the uniqueness is proved and the instability is characterized. To address this instability, we apply Tikhonov regularization, achieving stable numerical solutions and giving error estimates. Finally, numerical experiments demonstrate the effectiveness of the regularization method.
{"title":"An inverse random source problem for pseudo-parabolic equation of Caputo type with fractional-order Laplacian operator","authors":"Jiamin Lu, Liwen Xu, Hao Cheng","doi":"10.1016/j.cam.2026.117345","DOIUrl":"10.1016/j.cam.2026.117345","url":null,"abstract":"<div><div>In this paper, we investigate an inverse random source problem for the fractional pseudo-parabolic equation, where the source is driven by a fractional Brownian motion (fBm). For the direct problem, we illustrate the existence and uniqueness of the mild solution. For the inverse random source problem, the uniqueness is proved and the instability is characterized. To address this instability, we apply Tikhonov regularization, achieving stable numerical solutions and giving error estimates. Finally, numerical experiments demonstrate the effectiveness of the regularization method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117345"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979454","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 : 2026-08-15Epub Date: 2025-12-24DOI: 10.1016/j.cam.2025.117283
Liang Chen, Qiuqi Li, Hongyu Yang
This paper presents a non-intrusive model order reduction method based on nonlinear optimization for steady parameterized Stokes problems. To achieve this, we employ a weighted loss function to balance the velocity and pressure outputs to obtain a non-intrusive, data-driven algorithm utilizing only output samples. Moreover, we derive the gradients of the objective function with respect to the reduced-order matrices by resorting to the parameter-separable forms of reduced-model quantities. To enhance computational efficiency, our framework employs a two-stage offline-online decomposition. In the offline stage, we leverage gradient information to develop an optimization algorithm that computes optimal approximations for reduced-order matrices. In the online stage, the outputs can be quickly estimated for new parameter values using the reduced-order model obtained from the offline phase. Finally, we present numerical experiments to validate the effectiveness of this method, especially to demonstrate its capability to produce highly accurate approximation results.
{"title":"A non-intrusive model order reduction method based on nonlinear optimization for parameterized Stokes problems","authors":"Liang Chen, Qiuqi Li, Hongyu Yang","doi":"10.1016/j.cam.2025.117283","DOIUrl":"10.1016/j.cam.2025.117283","url":null,"abstract":"<div><div>This paper presents a non-intrusive model order reduction method based on nonlinear optimization for steady parameterized Stokes problems. To achieve this, we employ a weighted loss function to balance the velocity and pressure outputs to obtain a non-intrusive, data-driven algorithm utilizing only output samples. Moreover, we derive the gradients of the objective function with respect to the reduced-order matrices by resorting to the parameter-separable forms of reduced-model quantities. To enhance computational efficiency, our framework employs a two-stage offline-online decomposition. In the offline stage, we leverage gradient information to develop an optimization algorithm that computes optimal approximations for reduced-order matrices. In the online stage, the outputs can be quickly estimated for new parameter values using the reduced-order model obtained from the offline phase. Finally, we present numerical experiments to validate the effectiveness of this method, especially to demonstrate its capability to produce highly accurate approximation results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117283"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928222","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 : 2026-08-15Epub Date: 2025-12-30DOI: 10.1016/j.cam.2025.117316
Laura Selicato , Flavia Esposito , Andersen Ang , Nicoletta Del Buono , Rafał Zdunek
The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between reconstruction accuracy and adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, which is particularly effective for extracting low spectral density components from spectrograms of mixed signals, and benefits from the introduction of sparsity constraints. We propose a new algorithm called SHINBO, which introduces a bi-level optimization framework to automatically and adaptively tune the row-dependent penalty hyperparameters, enhancing the ability of IS-NMF to isolate sparse, periodic signals in noisy environments. Experimental results demonstrate that SHINBO achieves accurate spectral decompositions and demonstrates superior performance in both synthetic and real-world applications. In the latter case, SHINBO is particularly useful for noninvasive vibration-based fault detection in rolling bearings, where the desired signal components often reside in high-frequency subbands but are obscured by stronger, spectrally broader noise. By addressing the critical issue of hyperparameter selection, SHINBO improves the state-of-the-art in signal recovery for complex, noise-dominated environments.
{"title":"Sparse hyperparametric Itakura-Saito nonnegative matrix factorization via bi-level optimization","authors":"Laura Selicato , Flavia Esposito , Andersen Ang , Nicoletta Del Buono , Rafał Zdunek","doi":"10.1016/j.cam.2025.117316","DOIUrl":"10.1016/j.cam.2025.117316","url":null,"abstract":"<div><div>The selection of penalty hyperparameters is a critical aspect in Nonnegative Matrix Factorization (NMF), since these values control the trade-off between reconstruction accuracy and adherence to desired constraints. In this work, we focus on an NMF problem involving the Itakura-Saito (IS) divergence, which is particularly effective for extracting low spectral density components from spectrograms of mixed signals, and benefits from the introduction of sparsity constraints. We propose a new algorithm called SHINBO, which introduces a bi-level optimization framework to automatically and adaptively tune the row-dependent penalty hyperparameters, enhancing the ability of IS-NMF to isolate sparse, periodic signals in noisy environments. Experimental results demonstrate that SHINBO achieves accurate spectral decompositions and demonstrates superior performance in both synthetic and real-world applications. In the latter case, SHINBO is particularly useful for noninvasive vibration-based fault detection in rolling bearings, where the desired signal components often reside in high-frequency subbands but are obscured by stronger, spectrally broader noise. By addressing the critical issue of hyperparameter selection, SHINBO improves the state-of-the-art in signal recovery for complex, noise-dominated environments.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"482 ","pages":"Article 117316"},"PeriodicalIF":2.6,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928214","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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