Journal of Computational and Applied Mathematics最新文献_第2页

Weak dangling block reordering and multi-step block compression for efficiently computing and updating PageRank solutions 弱悬挂区块重排序和多步区块压缩，用于高效计算和更新 PageRank 解法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-25 DOI: 10.1016/j.cam.2024.116332

Zhao-Li Shen , Guo-Liang Han , Yu-Tong Liu , Bruno Carpentieri , Chun Wen , Jian-Jun Wang

{"title":"Weak dangling block reordering and multi-step block compression for efficiently computing and updating PageRank solutions","authors":"Zhao-Li Shen , Guo-Liang Han , Yu-Tong Liu , Bruno Carpentieri , Chun Wen , 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":null,"pages":null},"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}

引用次数: 0

On the numerical solution to space fractional differential equations using meshless finite differences 利用无网格有限差分法数值求解空间分数微分方程

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-24 DOI: 10.1016/j.cam.2024.116322

A. García , M. Negreanu , F. Ureña , A.M. Vargas

引用次数: 0

Efficient algorithms for perturbed symmetrical Toeplitz-plus-Hankel systems 扰动对称托普利兹加汉克尔系统的高效算法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-24 DOI: 10.1016/j.cam.2024.116333

Hcini Fahd , Skander Belhaj , Yulin Zhang

引用次数: 0

On general tempered fractional calculus with Luchko kernels 关于带有卢奇科内核的一般节制分数微积分

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-24 DOI: 10.1016/j.cam.2024.116339

Furqan Hussain, Mujeeb ur Rehman

引用次数: 0

Parallel cyclic reduction of padded bordered almost block diagonal matrices 填充式有边几乎对角分块矩阵的并行循环还原

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-24 DOI: 10.1016/j.cam.2024.116331

Enrico Bertolazzi, Davide Stocco

{"title":"Parallel cyclic reduction of padded bordered almost block diagonal matrices","authors":"Enrico Bertolazzi, 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":null,"pages":null},"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}

引用次数: 0

On the adaptive deterministic block Kaczmarz method with momentum for solving large-scale consistent linear systems 关于求解大规模一致线性系统的带动量的自适应确定性块卡兹马兹方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-23 DOI: 10.1016/j.cam.2024.116328

Longze Tan , Xueping Guo , Mingyu Deng , Jingrun Chen

{"title":"On the adaptive deterministic block Kaczmarz method with momentum for solving large-scale consistent linear systems","authors":"Longze Tan , Xueping Guo , Mingyu Deng , Jingrun Chen","doi":"10.1016/j.cam.2024.116328","DOIUrl":"10.1016/j.cam.2024.116328","url":null,"abstract":"<div><div>The Kaczmarz method is a traditional and widely used iterative algorithm for solving large-scale consistent linear systems, while its improved block Kaczmarz-type methods have received much attention and research in recent years due to their excellent numerical performance. Hence, in this paper, we present a deterministic block Kaczmarz method with momentum, which is based on Polyak’s heavy ball method and a row selection criterion for a set of block-controlled indices defined by the Euclidean norm of the residual vector. The proposed method does not need to compute the pseudo-inverses of a row submatrix at each iteration and it adaptively selects and updates the set of block control indices, thus this is different from the block Kaczmarz-type methods that are based on projection and pre-partitioning of row indices. The theoretical analysis of the proposed method shows that it converges linearly to the unique least-norm solutions of the consistent linear systems. Numerical experiments demonstrate that the deterministic block Kaczmarz method with momentum method is more efficient than the existing block Kaczmarz-type methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554470","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}

引用次数: 0

Detective generalized multiscale hybridizable discontinuous Galerkin(GMsHDG) method for porous media 探测多孔介质的广义多尺度可混合非连续伽勒金（GMsHDG）方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116320

Do Yang Park, Minam Moon

{"title":"Detective generalized multiscale hybridizable discontinuous Galerkin(GMsHDG) method for porous media","authors":"Do Yang Park, Minam Moon","doi":"10.1016/j.cam.2024.116320","DOIUrl":"10.1016/j.cam.2024.116320","url":null,"abstract":"<div><div>The Detective Generalized Multiscale Hybridizable Discontinuous Galerkin (Detective GMsHDG) method aims to further reduce the computational cost of the GMsHDG method. The GMsHDG method itself reduces the computational cost of the HDG method by employing an upscaled structure on a two-grid mesh. Given a PDE within a specified domain, we subdivide the domain into polygonal subdomains and transforms a HDG problem into globular and local problems. Globular problem concerns whether the solutions on smaller domains glue well to form a globular solution. The process involves generation of multiscale spaces, which is a vector space of functions defined on edges of the polygonal regions. A naive approximation by polynomials fails, especially in porous media, necessitating the generation of problem-specific spaces. The Detective GMsHDG method improves this process by replacing the generation of the multiscale space with the detective algorithm. The Detective GMsHDG method has two stages. First is called an offline stage. During the offline stage, we construct a detective function which, given a permeability distribution, it gives a multiscale space. Later stage is called the offline stage where, given the multiscale space, we use GMsHDG method to solve a given PDE numerically. We show numerical results to argue the liability of the solution using the detective GMsHDG method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532047","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}

引用次数: 0

A novel post-processed finite element method and its convergence for partial differential equations 新颖的后处理有限元方法及其对偏微分方程的收敛性

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116319

Wenming He , Jiming Wu , Zhimin Zhang

引用次数: 0

An efficient Newton-type matrix splitting algorithm for solving generalized absolute value equations with application to ridge regression problems 用于求解广义绝对值方程的高效牛顿型矩阵分割算法及其在脊回归问题中的应用

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116329

Xuehua Li, Cairong Chen

引用次数: 0

Dimension reduction based on time-limited cross Gramians for bilinear systems 基于双线性系统的限时交叉格拉米安法降维

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-10-16 DOI: 10.1016/j.cam.2024.116302

Zhi-Hua Xiao , Yao-Lin Jiang , Zhen-Zhong Qi

引用次数: 0