Journal of Computational and Applied Mathematics最新文献

{"title":"A first order dynamical system and its discretization for a class of variational inequalities","authors":"Nguyen Buong","doi":"10.1016/j.cam.2024.116341","DOIUrl":"10.1016/j.cam.2024.116341","url":null,"abstract":"<div><div>In this paper, we study the variational inequality problem over the set of common fixed points of a Lipschitz continuous pseudo-contraction and a finite family of strictly pseudo-contractive operators on a real Hilbert space. We introduce a first order dynamical system in accordance with the Lavrentiev regularization method. The existence and strong convergence with a discretized variant of the trajectory of the dynamical system are proved under some mild conditions. Applications to solving the convex constrained monotone equations and to the LASSO problem with numerical experiments are given for validating our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116341"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572662","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":"Statistical inference on the cumulative distribution function using judgment post stratification","authors":"Mina Azizi Kouhanestani ,&nbsp;Ehsan Zamanzade ,&nbsp;Sareh Goli","doi":"10.1016/j.cam.2024.116340","DOIUrl":"10.1016/j.cam.2024.116340","url":null,"abstract":"<div><div>In this work, we discuss a general class of estimators for the cumulative distribution function (CDF) based on judgment post stratification (JPS) sampling scheme, which includes both empirical and kernel distribution functions. Specifically, we obtain the expectation of the estimators in this class and show that they are asymptotically more efficient than their competitors in simple random sampling (SRS), as long as the rankings are better than random guessing. We find a mild condition that is necessary and sufficient for them to be asymptotically unbiased. We also prove that given the same condition, the estimators in this class are strongly uniformly consistent estimators of the true CDF, and converge in distribution to a normal distribution when the sample size approaches infinity. We then focus on the kernel distribution function (KDF) in the JPS design and obtain the optimal bandwidth. We next carry out a comprehensive Monte Carlo simulation to compare the performance of the KDF in the JPS design for different choices of sample size, set size, ranking quality, parent distribution, kernel function, as well as both perfect and imperfect rankings set-ups, with its counterpart in the SRS design. We find that the JPS estimator dramatically improves the efficiency of the KDF compared to its SRS competitor across a wide range of the settings. Finally, we apply the described procedure to a real dataset from a medical context to show its usefulness and applicability in practice.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116340"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578377","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 efficient modified conjugate gradient algorithm under Wolfe conditions with applications in compressive sensing","authors":"Zhibin Zhu ,&nbsp;Jiaqi Huang ,&nbsp;Ying Liu ,&nbsp;Yuehong Ding","doi":"10.1016/j.cam.2024.116335","DOIUrl":"10.1016/j.cam.2024.116335","url":null,"abstract":"<div><div>This paper presents a new modified conjugate gradient (NMCG) algorithm which satisfies the sufficient descent property under any line search for unconstrained optimization problems. We analyze that the algorithm is global convergence under the Wolfe line search. We use the proposed algorithm NMCG to unconstrained optimization problems to prove its effectiveness. Furthermore, we also extend it to solve image restoration and sparse signal recovery problems in compressive sensing, and the results indicate that our algorithm is effective and competitive.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116335"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572660","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":"Superconvergent results for fractional Volterra integro-differential equations with non-smooth solutions","authors":"Ruby,&nbsp;Moumita Mandal","doi":"10.1016/j.cam.2024.116337","DOIUrl":"10.1016/j.cam.2024.116337","url":null,"abstract":"<div><div>This article focuses on finding the approximate solutions of fractional Volterra integro-differential equations with non-smooth solutions using the shifted Jacobi spectral Galerkin method (SJSGM) and its iterated version. To deal with the singularity present in the kernel of the transformed weakly singular Volterra integral equation, we convert it into an equivalent weakly singular Fredholm integral equation. We first directly apply our proposed methods to this equivalent transformed equation and obtain improved convergence results by incorporating the singularity of the kernel function into the shifted Jacobi weight function. Further, we introduce a smoothing transformation and discuss the regularity of the transformed solution, and achieve superconvergence results for all <span><math><mrow><mi>γ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Additionally, we obtain super-convergence results for classical first-order Volterra integro-differential equations. Finally, numerical examples with a comparative study are provided to validate our theoretical results and verify the efficiency of the proposed methods. We show that the convergence rates can be obtained to the desired degree by increasing the value of the smoothing index <span><math><mi>ϱ</mi></math></span> <span><math><mrow><mo>(</mo><mn>1</mn><mo>&lt;</mo><mi>ϱ</mi><mo>∈</mo><mi>N</mi><mo>)</mo></mrow></math></span>, where <span><math><mi>N</mi></math></span> stands for the set of natural numbers.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116337"},"PeriodicalIF":2.1,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554747","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":"Deterministic computation of quantiles in a Lipschitz framework","authors":"Yurun Gu ,&nbsp;Clément Rey","doi":"10.1016/j.cam.2024.116344","DOIUrl":"10.1016/j.cam.2024.116344","url":null,"abstract":"<div><div>In this article, we focus on computing the quantiles of a random variable <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>X</mi></math></span> is a <span><math><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup></math></span>-valued random variable, <span><math><mrow><mi>d</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, and <span><math><mrow><mi>f</mi><mo>:</mo><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>d</mi></mrow></msup><mo>→</mo><mi>R</mi></mrow></math></span> is a deterministic Lipschitz function. We are particularly interested in scenarios where the cost of a single function evaluation is high, while the law of <span><math><mi>X</mi></math></span> is assumed to be known. In this context, we propose a deterministic algorithm to compute deterministic lower and upper bounds for the quantile of <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math></span> at a given level <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. With a fixed budget of <span><math><mi>N</mi></math></span> function calls, we demonstrate that our algorithm achieves an exponential deterministic convergence rate for <span><math><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></math></span> (<span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>ρ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>) and a polynomial deterministic convergence rate for <span><math><mrow><mi>d</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span> (<span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow></mrow></math></span>) and show the optimality of those rates. Furthermore, we design two algorithms, depending on whether the Lipschitz constant of <span><math><mi>f</mi></math></span> is known or unknown.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116344"},"PeriodicalIF":2.1,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weak dangling block reordering and multi-step block compression for efficiently computing and updating PageRank solutions","authors":"Zhao-Li Shen ,&nbsp;Guo-Liang Han ,&nbsp;Yu-Tong Liu ,&nbsp;Bruno Carpentieri ,&nbsp;Chun Wen ,&nbsp;Jian-Jun Wang","doi":"10.1016/j.cam.2024.116332","DOIUrl":"10.1016/j.cam.2024.116332","url":null,"abstract":"<div><div>The PageRank model is a powerful tool for network analysis, utilized across various disciplines such as web information retrieval, bioinformatics, community detection, and graph neural network. Computing this model requires solving a large-dimensional linear system or eigenvector problem due to the ever-increasing scale of networks. Conventional preconditioners and iterative methods for general linear systems or eigenvector problems often exhibit unsatisfactory performance for such problems, particularly as the damping factor parameter approaches 1, necessitating the development of specialized methods that exploit the specific properties of the PageRank coefficient matrix. Additionally, in practical applications, the optimal settings of the hyperparameters are generally unknown in advance, and networks often evolve over time. Consequently, recomputation of the problem is necessary following minor modifications. In this scenario, highly efficient preconditioners that significantly accelerate the iterative solution at a low memory cost are desirable. In this paper, we present two techniques that leverage the sparsity structures and numerical properties of the PageRank system, as well as a preconditioner based on the computed matrix structure. Experiments demonstrate the positive performance of the proposed methods on realistic PageRank computations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116332"},"PeriodicalIF":2.1,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the numerical solution to space fractional differential equations using meshless finite differences","authors":"A. García ,&nbsp;M. Negreanu ,&nbsp;F. Ureña ,&nbsp;A.M. Vargas","doi":"10.1016/j.cam.2024.116322","DOIUrl":"10.1016/j.cam.2024.116322","url":null,"abstract":"<div><div>We derive a discretization of the Caputo and Riemann–Liouville spatial derivatives by means of the meshless Generalized Finite Difference Method, which is based on moving least squares. The conditional convergence of the method is proved and several examples over one dimensional irregular meshes are given.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"457 ","pages":"Article 116322"},"PeriodicalIF":2.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient algorithms for perturbed symmetrical Toeplitz-plus-Hankel systems","authors":"Hcini Fahd ,&nbsp;Skander Belhaj ,&nbsp;Yulin Zhang","doi":"10.1016/j.cam.2024.116333","DOIUrl":"10.1016/j.cam.2024.116333","url":null,"abstract":"<div><div>This paper investigates a specific class of perturbed Toeplitz-plus-Hankel matrices. We introduce two novel algorithms designed for perturbed symmetrical centrosymmetrical Toeplitz-plus-Hankel systems, offering reduced computational time. Furthermore, we present applications of image encryption and decryption based on these algorithms. Through numerical experiments, we demonstrate the effectiveness of our proposed algorithms.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"457 ","pages":"Article 116333"},"PeriodicalIF":2.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On general tempered fractional calculus with Luchko kernels","authors":"Furqan Hussain,&nbsp;Mujeeb ur Rehman","doi":"10.1016/j.cam.2024.116339","DOIUrl":"10.1016/j.cam.2024.116339","url":null,"abstract":"<div><div>In this paper, we construct the <span><math><mi>n</mi></math></span>-fold <span><math><mi>ψ</mi></math></span>-fractional integrals and derivatives and study their properties. This construction is purely based on the approach proposed by Luchko (2021). The fundamental theorems of fractional calculus are formulated and proved for the proposed <span><math><mi>n</mi></math></span>-fold <span><math><mi>ψ</mi></math></span>-fractional integrals and derivatives. On the other hand, a suitable generalization of the Luchko condition is presented to discuss the <span><math><mi>ψ</mi></math></span>-tempered fractional calculus of arbitrary order. We introduce an important class of kernels that satisfy this condition. For the <span><math><mi>ψ</mi></math></span>-tempered fractional integrals and derivatives of arbitrary order, two fundamental theorems are proven, along with a relation between Riemann–Liouville and Caputo derivatives. Finally, Cauchy problems for the fractional differential equations with the <span><math><mi>ψ</mi></math></span>-tempered fractional derivatives are solved.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116339"},"PeriodicalIF":2.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554749","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":"Parallel cyclic reduction of padded bordered almost block diagonal matrices","authors":"Enrico Bertolazzi,&nbsp;Davide Stocco","doi":"10.1016/j.cam.2024.116331","DOIUrl":"10.1016/j.cam.2024.116331","url":null,"abstract":"<div><div>The solution of linear systems is a crucial and indispensable technique in the field of numerical analysis. Among linear system solvers, the cyclic reduction algorithm stands out for its natural inclination to parallelization. So far, the cyclic reduction has been applied primarily to linear systems with almost block diagonal matrices. Some of its variants widen the usage to almost block diagonal matrices with a last block of rows introducing a set of non-zero elements in the first group of columns. In this work, we extend cyclic reduction to matrices with additional non-zero elements below and to the right without any limitations. These matrices, called padded bordered almost block diagonal, arise from the discretization of optimal control problems featuring arbitrary boundary conditions and free parameters. Nonetheless, they also appear in two-point boundary value problems with free parameters. The proposed algorithm is based on the LU factorizations, and it is designed to be executed in parallel on multi-thread architectures. The algorithm performance is assessed through numerical experiments with different matrix sizes and threads. The computation times and speedups obtained with the parallel implementation indicate that the suggested algorithm is a robust solution for solving padded bordered almost block diagonal linear systems. Furthermore, its structure makes it suitable for the use of different matrix factorization techniques, such as QR or SVD. This flexibility enables tailored customization of the algorithm on the basis of the specific application requirements.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116331"},"PeriodicalIF":2.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}