Journal of Computational and Applied Mathematics最新文献

英文中文

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 Q1 MATHEMATICS, APPLIED

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

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.

PageRank 模型是一种强大的网络分析工具，广泛应用于网络信息检索、生物信息学、群落检测和图神经网络等多个学科。由于网络规模不断扩大，计算该模型需要求解一个大维度线性系统或特征向量问题。针对一般线性系统或特征向量问题的传统预处理和迭代方法在此类问题上的表现往往不能令人满意，尤其是当阻尼系数参数接近 1 时，因此有必要开发利用 PageRank 系数矩阵特定属性的专门方法。此外，在实际应用中，超参数的最佳设置通常是事先未知的，而且网络往往会随着时间的推移而演变。因此，在稍作修改后，必须重新计算问题。在这种情况下，我们需要高效的前提条件器，以较低的内存成本显著加速迭代求解。在本文中，我们介绍了利用 PageRank 系统的稀疏性结构和数值特性的两种技术，以及基于计算矩阵结构的前置条件器。实验证明了所提方法在实际 PageRank 计算中的良好性能。

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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 Q1 MATHEMATICS, APPLIED

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

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.

我们通过基于移动最小二乘法的无网格广义有限差分法，推导出了卡普托和黎曼-刘维尔空间导数的离散化方法。证明了该方法的条件收敛性，并给出了一维不规则网格上的几个实例。

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 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-24 DOI: 10.1016/j.cam.2024.116333

Hcini Fahd , Skander Belhaj , Yulin Zhang

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.

本文研究了一类特殊的扰动托普利兹-加-汉克尔矩阵。我们介绍了为扰动对称中心对称 Toeplitz-plus-Hankel 系统设计的两种新算法，它们能缩短计算时间。此外，我们还介绍了基于这些算法的图像加密和解密应用。通过数值实验，我们证明了所提算法的有效性。

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 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-24 DOI: 10.1016/j.cam.2024.116339

Furqan Hussain, Mujeeb ur Rehman

In this paper, we construct the

n

-fold

ψ

-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

n

-fold

ψ

-fractional integrals and derivatives. On the other hand, a suitable generalization of the Luchko condition is presented to discuss the

ψ

-tempered fractional calculus of arbitrary order. We introduce an important class of kernels that satisfy this condition. For the

ψ

-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

ψ

-tempered fractional derivatives are solved.

在本文中，我们构建了 n 重 ψ 分积分和导数，并研究了它们的性质。这一构造完全基于 Luchko（2021）提出的方法。针对所提出的 n 折 ψ-分式积分和导数，提出并证明了分式微积分的基本定理。另一方面，提出了卢奇科条件的适当广义化，以讨论任意阶的ψ温带分数微积分。我们介绍了满足这一条件的一类重要的核。对于任意阶的ψ回火分数积分和导数，证明了两个基本定理，以及黎曼-刘维尔导数和卡普托导数之间的关系。最后，还求解了带有 ψ 调和分数导数的分数微分方程的 Cauchy 问题。

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 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-24 DOI: 10.1016/j.cam.2024.116331

Enrico Bertolazzi, Davide Stocco

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.

线性系统求解是数值分析领域不可或缺的关键技术。在线性系统求解器中，循环缩减算法因其天然的并行化倾向而脱颖而出。迄今为止，循环缩减主要应用于矩阵几乎为对角线的线性系统。它的一些变体将其应用范围扩大到了在第一组列中引入一组非零元素的最后一组行的几乎是对角线的矩阵。在这项工作中，我们将循环缩减扩展到下面和右边有额外非零元素的矩阵，没有任何限制。这些矩阵被称为有边框的近似块对角矩阵，产生于具有任意边界条件和自由参数的最优控制问题的离散化。不过，它们也出现在具有自由参数的两点边界值问题中。所提出的算法以 LU 因子化为基础，可在多线程架构上并行执行。算法性能通过不同矩阵大小和线程的数值实验进行评估。并行执行所获得的计算时间和速度提升表明，所建议的算法是解决填充边界几乎对角线块线性系统的稳健解决方案。此外，该算法的结构使其适合使用不同的矩阵因式分解技术，如 QR 或 SVD。这种灵活性使算法可以根据具体应用要求进行定制。

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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 Q1 MATHEMATICS, APPLIED

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

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.

Kaczmarz 方法是一种传统的、广泛应用于求解大规模一致线性系统的迭代算法，而其改进的块 Kaczmarz 型方法由于其优异的数值性能，近年来受到了广泛的关注和研究。因此，在本文中，我们提出了一种带动量的确定性块 Kaczmarz 方法，该方法基于 Polyak 的重球方法和一组由残差向量的欧氏规范定义的块控制指数的行选择准则。所提出的方法无需在每次迭代时计算行子矩阵的伪反演，而且可以自适应地选择和更新块控制指数集，因此不同于基于行指数的投影和预分区的块 Kaczmarz 型方法。对所提方法的理论分析表明，该方法线性收敛于一致线性系统的唯一最小规范解。数值实验证明，带动量法的确定性块 Kaczmarz 方法比现有的块 Kaczmarz 类型方法更有效。

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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 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116320

Do Yang Park, Minam Moon

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.

Detective Generalized Multiscale Hybridizable Discontinuous Galerkin（Detective GMsHDG）方法旨在进一步降低 GMsHDG 方法的计算成本。GMsHDG 方法本身通过在双网格上采用放大结构降低了 HDG 方法的计算成本。给定域内的一个 PDE，我们将域细分为多边形子域，并将 HDG 问题转化为球状问题和局部问题。全局问题涉及较小域上的解是否能很好地粘合以形成全局解。这一过程包括生成多尺度空间，即定义在多边形区域边缘上的函数向量空间。用多项式进行天真的近似是失败的，尤其是在多孔介质中，因此必须生成特定问题的空间。通过用侦探算法取代多尺度空间的生成，侦探式 GMsHDG 方法改进了这一过程。Detective GMsHDG 方法分为两个阶段。第一个阶段称为离线阶段。在离线阶段，我们构建一个侦探函数，在给定渗透率分布的情况下，给出一个多尺度空间。后一阶段称为离线阶段，在这一阶段，给定多尺度空间后，我们使用 GMsHDG 方法对给定的 PDE 进行数值求解。我们将展示数值结果，以论证使用 GMsHDG 侦探方法求解的可行性。

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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 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116319

Wenming He , Jiming Wu , Zhimin Zhang

In this article, by combining high-order interpolation on coarse meshes and low-order finite element solutions on fine meshes, we propose a novel approach to improve the accuracy of the finite element method. The new method is in general suitable for most partial differential equations. For simplicity, we use the second-order elliptic problem as an example to show how the novel approach improves the accuracy of the finite element method. Numerical tests are also conducted to validate the main theoretical results.

本文结合粗网格上的高阶插值和细网格上的低阶有限元求解，提出了一种提高有限元方法精度的新方法。新方法一般适用于大多数偏微分方程。为简单起见，我们以二阶椭圆问题为例，说明新方法如何提高有限元方法的精度。我们还进行了数值测试，以验证主要理论结果。

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 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116329

Xuehua Li, Cairong Chen

A generalized Newton-based matrix splitting (GNMS) method is proposed for solving the generalized absolute value equations (GAVEs). Under mild conditions, the GNMS method converges to the unique solution of GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.

本文提出了一种求解广义绝对值方程（GAVE）的基于牛顿的广义矩阵分割（GNMS）方法。在温和条件下，GNMS 方法能收敛到广义绝对值方程的唯一解。此外，我们还可以得到一些现有方法的较弱收敛条件。数值结果验证了所提方法的有效性。

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 Q1 MATHEMATICS, APPLIED

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

The cross Gramian is a useful tool in model order reduction but only applicable to square dynamical systems. Throughout this paper, time-limited cross Gramians is firstly extended to square bilinear systems that satisfies a generalized Sylvester equation, and then concepts from decentralized control are used to approximate a cross Gramian for non-square bilinear systems. In order to illustrate these cross Gramians, they are calculated efficiently based on shifted Legendre polynomials and applied to dimension reduction, which leads to a lower dimensional model by truncating the states that are associated with smaller approximate generalized Hankel singular values. In combination of the dominant subspace projection method, our reduction procedure is modified to produce a bounded-input bounded-output stable-preserved reduced model under some certain conditions. At last, the performance of numerical experiments indicates the validity of our reduction methods.

交叉格拉米安是减少模型阶次的有用工具，但只适用于方形动力系统。本文首先将限时交叉格拉米安扩展到满足广义西尔维斯特方程的平方双线性系统，然后利用分散控制的概念来近似非平方双线性系统的交叉格拉米安。为了说明这些交叉格拉米安，我们基于移位 Legendre 多项式对其进行了有效计算，并将其应用于降维，通过截断与较小的近似广义汉克尔奇异值相关的状态，从而得到一个低维模型。结合主导子空间投影法，我们的降维程序经过修改，在某些特定条件下产生了有界输入有界输出的稳定保留降维模型。最后，数值实验结果表明我们的还原方法是有效的。

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全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

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Journal of Computational and Applied Mathematics

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