Journal of Computational and Applied Mathematics最新文献

{"title":"Subsampling for tensor least squares: Optimization and statistical perspectives","authors":"Ling Tang ,&nbsp;Hanyu Li","doi":"10.1016/j.cam.2025.116694","DOIUrl":"10.1016/j.cam.2025.116694","url":null,"abstract":"<div><div>In this paper, we propose the random subsampling method for tensor least squares problem with respect to the popular t-product. From the optimization perspective, we give the error bounds in the sense of probability for the solution and residual obtained by the proposed method. This perspective only considers the randomness of sampling, and the results indicate that leverage score sampling is superior to uniform sampling. From the statistical perspective, we derive the expressions of the conditional and unconditional expectations and variances for the solution. This perspective takes into account the randomness of both sampling and model noises simultaneously, and the results show that the unconditional variances for uniform sampling and leverage score sampling are both large and neither of them is dominant. In view of this, an optimal subsampling probability distribution is obtained by minimizing the trace of the unconditional variance. Finally, the feasibility and effectiveness of the proposed method and the correctness of the theoretical results are verified by numerical experiments.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116694"},"PeriodicalIF":2.1,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143877186","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 spectral Hestenes–Stiefel CG algorithm for large-scale unconstrained optimization in image restoration problems","authors":"Yuting Chen","doi":"10.1016/j.cam.2025.116709","DOIUrl":"10.1016/j.cam.2025.116709","url":null,"abstract":"<div><div>This paper presents a new method, termed spectral Hestenes-Stiefel conjugate gradient method, for large-scale unconstrained optimization. The generated direction automatically satisfies the sufficient descent property at each iteration, independent of the line searches employed or the convexity of the objective functions. Under standard conditions, the global convergence of the proposed method for general functions can be guaranteed. Numerical experiments are conducted on a set of unconstrained optimization problems with a maximum dimension of 600,000 to assess the effectiveness of the present method. Furthermore, the method is tested on four image restoration problems characterized by varying noise levels. The corresponding numerical results indicate that the encouraging efficiency and promising applicability of the developed method when compared to several existing methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116709"},"PeriodicalIF":2.1,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870402","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":"Reliability evaluation of multi-state (k1,k2,…,km)-out-of-(n1,n2,…,nm) system with common bus performance sharing","authors":"Yanjie Shi,&nbsp;Zaizai Yan","doi":"10.1016/j.cam.2025.116704","DOIUrl":"10.1016/j.cam.2025.116704","url":null,"abstract":"<div><div>The reliability of multi-state <span><math><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow></math></span>-out-of-<span><math><mrow><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow></math></span> system with performance sharing is investigated in this paper. The system consists of <span><math><mi>m</mi></math></span> types of components, comprising a total of <span><math><mi>n</mi></math></span> components, where each type <span><math><mi>i</mi></math></span> contains <span><math><msub><mrow><mi>n</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> components. The system work normally only if at least <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> components performance in each type <span><math><mi>i</mi></math></span> satisfy the random demands. Two stages of performance transmission are considered in the paper. In the first stage, surplus performance (SP) of components within the same type is transmitted to performance deficiency (PD) components via the common bus without any performance loss. In the second stage, after performance sharing within the same type is complete, the SP between different types can be transmitted to other types with PD through other common bus. At the same time, the loss of performance transmit between different types is considered. The reliability of the <span><math><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow></math></span>-out-of-<span><math><mrow><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow></math></span> system is assessed using the universal generating function (UGF) approach. Finally, numerical analysis and collaborative computer system as example are conducted to demonstrate the effectiveness of the proposed model and method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116704"},"PeriodicalIF":2.1,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860507","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":"Sharp estimates for the convergence rate of Orthomin(k) for a class of linear systems","authors":"Andrei Drăgănescu ,&nbsp;Florin Spinu","doi":"10.1016/j.cam.2025.116699","DOIUrl":"10.1016/j.cam.2025.116699","url":null,"abstract":"<div><div>In this work we show that the convergence rate of Orthomin(<span><math><mi>k</mi></math></span>) applied to systems of the form <span><math><mrow><mrow><mo>(</mo><mi>I</mi><mo>+</mo><mi>ρ</mi><mi>U</mi><mo>)</mo></mrow><mi>x</mi><mo>=</mo><mi>b</mi></mrow></math></span>, where <span><math><mi>U</mi></math></span> is a unitary operator and <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>ρ</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, is less than or equal to <span><math><mi>ρ</mi></math></span>. Moreover, we give examples of operators <span><math><mi>U</mi></math></span> and <span><math><mrow><mi>ρ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> for which the asymptotic convergence rate of Orthomin(<span><math><mi>k</mi></math></span>) is exactly <span><math><mi>ρ</mi></math></span>, thus showing that the estimate is sharp. While the systems under scrutiny may not be of great interest in themselves, their existence shows that, in general, Orthomin(<span><math><mi>k</mi></math></span>) does not converge faster than Orthomin(1). Furthermore, we give examples of systems for which Orthomin(<span><math><mi>k</mi></math></span>) has the same asymptotic convergence rate as Orthomin(2) for <span><math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, but smaller than that of Orthomin(1). The latter systems are related to the numerical solution of certain partial differential equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116699"},"PeriodicalIF":2.1,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863985","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":"Convergence analysis of a stochastic heavy-ball method for linear ill-posed problems","authors":"Qinian Jin,&nbsp;Yanjun Liu","doi":"10.1016/j.cam.2025.116702","DOIUrl":"10.1016/j.cam.2025.116702","url":null,"abstract":"<div><div>In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under <em>a priori</em> selection of the stopping index and derive the rate of convergence under a benchmark source condition on the sought solution. Numerical results are provided to test the performance of the method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116702"},"PeriodicalIF":2.1,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870585","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":"The generalized Drazin inverse of the sum of two elements in a Banach algebra","authors":"Daochang Zhang ,&nbsp;Yue Zhao ,&nbsp;Dijana Mosić","doi":"10.1016/j.cam.2025.116701","DOIUrl":"10.1016/j.cam.2025.116701","url":null,"abstract":"<div><div>In this paper, we present new additive results on the generalized Drazin inverse of a sum of two Banach algebra elements under certain conditions, which can generalize and unify some results. Then, we apply these additive results to derive explicit formulae for the generalized Drazin inverse of a 2 × 2 matrix <span><math><mfenced><mrow><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mrow></mfenced></math></span> in a Banach algebra. Finally, several numerical examples are given to illustrate our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116701"},"PeriodicalIF":2.1,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870591","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 indefinite proximal Peaceman–Rachford splitting method-based algorithm integrating the generalization acceleration technique for separable convex programming problems in image restoration","authors":"Xianke Tang ,&nbsp;Jianghua Yin ,&nbsp;Dan Jian ,&nbsp;Daolan Han","doi":"10.1016/j.cam.2025.116693","DOIUrl":"10.1016/j.cam.2025.116693","url":null,"abstract":"<div><div>In this paper, we consider the linearly constrained separable convex optimization problem, where the objective function is the sum of two individual extended real-valued functions without coupled variables. Based on the common convex combination technique and with the help of the indefinite proximal regularization technique, we propose a novel Peaceman–Rachford splitting method (PRSM). The generalization acceleration technique is integrated into the proximal term of the first subproblem, where the proximal matrix could be positive semidefinite so as to ensure the solution existence of the just-mentioned subproblem. Moreover, we allow the proximal matrix in the second subproblem to be indefinite but still guaranteeing the convergence of the proposed method theoretically. It is worth to mention that the range of the coefficient for the generalization acceleration step can be extended from <span><math><mrow><mo>[</mo><mn>0</mn><mo>.</mo><mn>618</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> to <span><math><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>. Under some mild conditions, we establish the global convergence and ergodic <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mo>)</mo></mrow></mrow></math></span> sublinear convergence rate measured by the function value residual and constraint violation, where <span><math><mi>N</mi></math></span> denotes the number of iterations. To our knowledge, this is the first time that the generalization acceleration technique has been used to accelerate the convergence of PRSM-based methods. Finally, numerical experiments allow to verify the effectiveness of the proposed algorithm in solving LASSO and total variation image restoration problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116693"},"PeriodicalIF":2.1,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870401","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 frequency-independent solver for systems of linear ordinary differential equations","authors":"Tony Hu,&nbsp;James Bremer","doi":"10.1016/j.cam.2025.116696","DOIUrl":"10.1016/j.cam.2025.116696","url":null,"abstract":"<div><div>When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions generally exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing such solutions using standard techniques grows with the magnitudes of the eigenvalues. As a consequence, the running times of standard solvers for ordinary differential equations also grow with the size of these eigenvalues. The solutions of scalar equations with slowly-varying coefficients, however, can be represented via slowly-varying phase functions at a cost which is bounded independent of the magnitudes of the eigenvalues of the corresponding coefficient matrix. Here we couple an existing solver for scalar equations which exploits this observation with a well-known technique for transforming a system of linear ordinary differential equations into scalar form. The result is a method for solving a large class of systems of linear ordinary differential equations in time independent of the magnitudes of the eigenvalues of their coefficient matrices. We discuss the results of numerical experiments demonstrating the properties of our algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116696"},"PeriodicalIF":2.1,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864104","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 control of linear fractional differential equations in the Caputo sense","authors":"José Villa-Morales ,&nbsp;Luis Rincón ,&nbsp;Gerardo Becerra-Guzmán","doi":"10.1016/j.cam.2025.116707","DOIUrl":"10.1016/j.cam.2025.116707","url":null,"abstract":"<div><div>In this work, we study a time-optimal control problem involving bounded controls to regulate the dynamics of a linear fractional differential equation in the Caputo sense. We prove that the equation governing the dynamics admits optimal controls, which are of the bang–bang type. Additionally, we establish the validity of a maximum principle for determining the optimal control. The paper includes two application examples. The first example demonstrates that the optimal time can be achieved by appropriately selecting the fractional index. The second example illustrates that the choice between the classical and the fractional model may depend on the initial state of the dynamics.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116707"},"PeriodicalIF":2.1,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864105","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":"Invertible matrices under non-Archimedean absolute value and its inverse","authors":"Suhua Li,&nbsp;Chaoqian Li","doi":"10.1016/j.cam.2025.116700","DOIUrl":"10.1016/j.cam.2025.116700","url":null,"abstract":"<div><div>Invertible matrices play a crucial role in various areas of mathematics, science and engineering. Although there are many ways to determine whether a matrix is invertible or not, it is still a fundamental and an important research work in linear algebra, especially in large-scale numerical computations. Based on the non-Archimedean absolute value, we in this paper present a new class of invertible matrices called <em>doubly strictly diagonally dominant matrices under non-Archimedean absolute value</em> (<em>DSDD</em><span><math><msub><mrow></mrow><mrow><mi>n</mi><mo>.</mo><mi>A</mi><mo>.</mo></mrow></msub></math></span> <em>matrices</em>). It includes the <em>strictly diagonally dominant matrices under non-Archimedean absolute value</em> (<em>SDD</em><span><math><msub><mrow></mrow><mrow><mi>n</mi><mo>.</mo><mi>A</mi><mo>.</mo></mrow></msub></math></span> <em>matrices</em>) presented by Nica and Sprague in [The American Mathematical Monthly, 130 (2023) 267-275]. Some examples are given to show the relationships of <em>SDD</em><span><math><msub><mrow></mrow><mrow><mi>n</mi><mo>.</mo><mi>A</mi><mo>.</mo></mrow></msub></math></span> <em>matrices</em>, <em>DSDD</em><span><math><msub><mrow></mrow><mrow><mi>n</mi><mo>.</mo><mi>A</mi><mo>.</mo></mrow></msub></math></span> <em>matrices</em>, <em>SDD matrices</em> (<em>strictly diagonally dominant matrices under Archimedean absolute value</em>), <em>DSDD matrices</em> (<em>doubly strictly diagonally dominant matrices under Archimedean absolute value</em>), and <em>H-matrices</em>. Moreover, it is proved that the inverse of <em>DSDD</em><span><math><msub><mrow></mrow><mrow><mi>n</mi><mo>.</mo><mi>A</mi><mo>.</mo></mrow></msub></math></span> <em>matrices</em> is also <em>DSDD</em><span><math><msub><mrow></mrow><mrow><mi>n</mi><mo>.</mo><mi>A</mi><mo>.</mo></mrow></msub></math></span> in some cases, which displays remarkable difference with the inverse of <em>DSDD matrices</em> and <em>SDD matrices</em>.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"470 ","pages":"Article 116700"},"PeriodicalIF":2.1,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863984","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}