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Edge importance in complex networks 复杂网络中边缘的重要性
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-09 DOI: 10.1007/s11075-024-01881-1
Silvia Noschese, Lothar Reichel

Complex networks are made up of vertices and edges. The latter connect the vertices. There are several ways to measure the importance of the vertices, e.g., by counting the number of edges that start or end at each vertex, or by using the subgraph centrality of the vertices. It is more difficult to assess the importance of the edges. One approach is to consider the line graph associated with the given network and determine the importance of the vertices of the line graph, but this is fairly complicated except for small networks. This paper compares two approaches to estimate the importance of edges of medium-sized to large networks. One approach computes partial derivatives of the total communicability of the weights of the edges, where a partial derivative of large magnitude indicates that the corresponding edge may be important. Our second approach computes the Perron sensitivity of the edges. A high sensitivity signals that the edge may be important. The performance of these methods and some computational aspects are discussed. Applications of interest include to determine whether a network can be replaced by a network with fewer edges with about the same communicability.

复杂网络由顶点和边组成。后者连接顶点。有几种方法可以衡量顶点的重要性,例如,计算以每个顶点为起点或终点的边的数量,或使用顶点的子图中心性。评估边的重要性则更为困难。一种方法是考虑与给定网络相关的线图,并确定线图顶点的重要性,但除了小型网络外,这种方法相当复杂。本文比较了两种估算中型到大型网络边缘重要性的方法。其中一种方法是计算边缘权重的总可传播性的偏导数,偏导数的大小越大,说明相应的边缘可能越重要。我们的第二种方法是计算边缘的 Perron 敏感度。灵敏度高表明该边缘可能很重要。本文讨论了这些方法的性能和一些计算方面的问题。我们感兴趣的应用包括确定一个网络是否可以被一个边缘数量较少但通信能力大致相同的网络所取代。
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引用次数: 0
Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method 抛物线-抛物线罗宾-罗宾耦合法的离散时间导数估算
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-09 DOI: 10.1007/s11075-024-01902-z
Erik Burman, Rebecca Durst, Miguel A. Fernández, Johnny Guzmán, Sijing Liu

We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in Burman et al. (J. Numer. Math. 31(1):59–77, 2023) for a parabolic-parabolic interface problem and prove estimates for the discrete time derivatives of the scalar field in different norms. When the interface is flat and perpendicular to two of the edges of the domain we prove error estimates in the (H^2)-norm. Such estimates are key ingredients to analyze a defect correction method for the parabolic-parabolic interface problem. Numerical results are shown to support our findings.

我们考虑 Burman 等人(J. Numer. Math.Math.31(1):59-77, 2023)中提出并分析的抛物线-抛物线界面问题,并证明了不同规范下标量场离散时间导数的估计值。当界面平坦且垂直于域的两条边时,我们证明了在(H^2)规范下的误差估计。这些估计值是分析抛物线-抛物线界面问题缺陷修正方法的关键要素。数值结果表明支持我们的发现。
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引用次数: 0
Discrete non-commutative hungry Toda lattice and its application in matrix computation 离散非交换饥饿户田网格及其在矩阵计算中的应用
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-08 DOI: 10.1007/s11075-024-01915-8
Zheng Wang, Shi-Hao Li, Kang-Ya Lu, Jian-Qing Sun

In this paper, we plan to show an eigenvalue algorithm for block Hessenberg matrices by using the idea of non-commutative integrable systems and matrix-valued orthogonal polynomials. We introduce adjacent families of matrix-valued (theta )-deformed bi-orthogonal polynomials, and derive corresponding discrete non-commutative hungry Toda lattice from discrete spectral transformations for polynomials. It is shown that this discrete system can be used as a pre-precessing algorithm for block Hessenberg matrices. Besides, some convergence analysis and numerical examples of this algorithm are presented.

在本文中,我们计划利用非交换可积分系统和矩阵值正交多项式的思想,展示一种块海森伯矩阵的特征值算法。我们引入了相邻的矩阵值(theta)变形的双正交多项式族,并从多项式的离散谱变换推导出相应的离散非交换饿户田网格。研究表明,该离散系统可用作块海森伯矩阵的预处理算法。此外,还介绍了该算法的一些收敛分析和数值示例。
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引用次数: 0
Approximate moment functions for logistic stochastic differentialequations 逻辑随机微分方程的近似矩函数
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-07 DOI: 10.1007/s11075-024-01911-y
Coşkun Çetin, Jasmina Đorđević

In this paper, we introduce a method of successive approximations for moment functions of logistic stochastic differential equations. We first reduce the system of the corresponding moment functions to an infinite system of linear ordinary differential equations. Then, we determine certain upper and lower bounds on the moment functions, and utilize these bounds to solve the resulting systems approximately via suitable truncations, iterations and a local improvement step. After obtaining some general theoretical results on the error norms and describing a general algorithm for logistic SDE, we focus on stochastic Verhulst systems in numerical implementations. We compare their moment approximations with numerical solutions via simulation-based methods that include discretizations of the pathwise solutions as well as other convergent numerical procedures like semi-implicit split-step Euler methods.

本文介绍了逻辑随机微分方程矩函数的连续逼近方法。我们首先将相应的矩函数系统简化为线性常微分方程的无限系统。然后,我们确定矩函数的某些上界和下界,并利用这些界值通过适当的截断、迭代和局部改进步骤近似求解所得到的系统。在获得关于误差规范的一些一般理论结果并描述了逻辑 SDE 的一般算法之后,我们将重点放在数值实现中的随机 Verhulst 系统上。我们将其矩近似值与基于模拟的数值解法进行了比较,后者包括路径解的离散化以及其他收敛数值程序,如半隐式分步欧拉方法。
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引用次数: 0
A novel higher-order efficient computational method for pricing European and Asian options 为欧洲和亚洲期权定价的新型高阶高效计算方法
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-06 DOI: 10.1007/s11075-024-01909-6
Saurabh Bansal, Srinivasan Natesan

In this article, we present a fourth-order accurate numerical method for solving generalized Black-Scholes PDE describing European and Asian options. Initially, we discretize the time derivative by the Crank-Nicolson scheme, and then the resultant semi-discrete problem by the central difference scheme on uniform meshes. In order to enhance the order of convergence of the proposed scheme, we employ the Richardson extrapolation method, by using two different meshes to solve the fully discrete problem. The stability and convergence are studied. To validate the proposed technique, several numerical experiments are carried out.

本文提出了一种四阶精确数值方法,用于求解描述欧洲和亚洲期权的广义 Black-Scholes PDE。首先,我们采用 Crank-Nicolson 方案对时间导数进行离散化,然后在均匀网格上采用中心差分方案对所得到的半离散问题进行离散化。为了提高所提方案的收敛阶次,我们采用了 Richardson 外推法,通过使用两个不同的网格来求解完全离散问题。对稳定性和收敛性进行了研究。为了验证所提出的技术,我们进行了几次数值实验。
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引用次数: 0
Convergence analysis of the augmented Lagrangian method for $$ell _{p}$$ -norm cone optimization problems with $$p ge 2$$ 针对$$p ge 2$$的$$ell _{p}$$-norm圆锥优化问题的增强拉格朗日法的收敛性分析
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-06 DOI: 10.1007/s11075-024-01912-x
Benqi Liu, Kai Gong, Liwei Zhang

This paper focuses on the convergence analysis of the augmented Lagrangian method (ALM) for (varvec{ell }_{varvec{p}})-norm cone optimization problems. We investigate some properties of the augmented Lagrangian function and (varvec{ell }_{varvec{p}})-norm cone. Moreover, under the Jacobian uniqueness conditions, we prove that the local convergence rate of ALM for solving (varvec{ell }_{varvec{p}})-norm cone optimization problems with (varvec{p} varvec{ge } varvec{2}) is proportional to (varvec{1}varvec{/}varvec{r}), where the penalty parameter (varvec{r}) is not less than a threshold (varvec{hat{r}}). In numerical simulations, we successfully validate the effectiveness and convergence properties of ALM.

本文主要研究了针对 (varvec{ell }_varvec{p}}-orm cone 优化问题的增强拉格朗日法(ALM)的收敛性分析。我们研究了增强拉格朗日函数和(varvec{ell }_{varvec{p}})-规范锥的一些特性。此外,在雅各布唯一性条件下,我们证明了 ALM 在求解 (varvec{ell }_{varvec{p}})-norm cone 优化问题时的局部收敛率与 (varvec{p} varvec{ge } varvec{2}) 成正比、其中,惩罚参数 (varvec{r})不小于阈值 (varvec{hat{r}})。在数值模拟中,我们成功验证了 ALM 的有效性和收敛性。
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引用次数: 0
A hybrid algorithm for computing a partial singular value decomposition satisfying a given threshold 计算满足给定阈值的部分奇异值分解的混合算法
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-06 DOI: 10.1007/s11075-024-01906-9
James Baglama, Jonathan A. Chávez-Casillas, Vasilije Perović

In this paper, we describe a new hybrid algorithm for computing all singular triplets above a given threshold and provide its implementation in MATLAB/Octave and R. The high performance of our codes and ease at which they can be used, either independently or within a larger numerical scheme, are illustrated through several numerical examples with applications to matrix completion and image compression. Well-documented MATLAB and R codes are provided for public use.

在本文中,我们描述了一种用于计算超过给定阈值的所有奇异三元组的新型混合算法,并提供了该算法在 MATLAB/Octave 和 R 中的实现。我们通过几个应用于矩阵补全和图像压缩的数值示例,说明了我们的代码的高性能及其在独立或更大数值方案中的易用性。我们提供了文档齐全的 MATLAB 和 R 代码供公众使用。
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引用次数: 0
Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions 非全局 Lipschitz 条件下随机微分方程随机周期解的随机 Theta 方法
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-05 DOI: 10.1007/s11075-024-01892-y
Ziheng Chen, Liangmin Cao, Lin Chen

This work focuses on the numerical approximations of random periodic solutions of stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove the existence and uniqueness of random periodic solutions for the considered equations and its numerical approximations generated by the stochastic theta (ST) methods with (theta in (1/2,1]). It is shown that the random periodic solution of each ST method converges strongly in the mean square sense to that of SDEs. More precisely, the mean square convergence order is 1/2 for SDEs with multiplicative noise and 1 for SDEs with additive noise, respectively. Numerical results are finally reported to confirm these theoretical findings.

这项研究的重点是随机微分方程(SDE)的随机周期解的数值近似。在非全局 Lipschitz 条件下,我们证明了所考虑方程的随机周期解的存在性和唯一性,以及由 theta in (1/2,1]) 随机θ(ST)方法产生的随机周期解的数值近似。结果表明,每种 ST 方法的随机周期解在均方意义上都强烈收敛于 SDE 的随机周期解。更准确地说,对于乘性噪声的 SDE 和加性噪声的 SDE,其均方收敛阶数分别为 1/2 和 1。最后报告的数值结果证实了这些理论发现。
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引用次数: 0
Optimization algorithms for stabilization of multi-input vibration system with time delay using eigenvalues assignment technique 利用特征值分配技术实现具有时间延迟的多输入振动系统稳定的优化算法
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-02 DOI: 10.1007/s11075-024-01899-5
Peizhao Yu, Fuheng Zhao, Haoming Xin

The study considers the robust and minimum norm problems for stabilization using partial eigenvalue assignment technique in nonsingular vibration system with time delay via the acceleration-velocity-displacement active controller. The new gains expressions of active controller are derived by orthogonality relations, which keeps the no spill-over property of the vibration system. To discuss the stabilization problem using eigenvalues assignment technique, the linear equation is solved by constructing a special matrix which is proved to be nonsingular. Solving algorithm is proposed to obtain the parametric expressions of active controller. A new gradient-based optimization method is proposed to discuss the robust and minimum norm controller design by establishing the gradient formulas of cost functions. The optimization algorithm is proposed to discuss the robust and minimum norm stabilization of closed-loop eigenvalues in vibration system with time delay. The presented algorithms are feasible to the case of time delay between measurements of state and actuation of control. Numerical examples show the effectiveness of the method.

该研究通过加速度-速度-位移主动控制器,利用部分特征值赋值技术考虑了有时间延迟的非正弦振动系统的鲁棒性和最小规范稳定问题。通过正交关系导出了主动控制器的新增益表达式,从而保持了振动系统的无溢出特性。为了利用特征值赋值技术讨论稳定问题,通过构建一个特殊矩阵来求解线性方程,该矩阵被证明是非奇异矩阵。提出了求解算法,以获得主动控制器的参数表达式。提出了一种新的基于梯度的优化方法,通过建立成本函数的梯度公式来讨论鲁棒和最小规范控制器的设计。提出了一种优化算法来讨论有时间延迟的振动系统中闭环特征值的鲁棒性和最小规范稳定问题。所提出的算法适用于状态测量和控制执行之间存在时间延迟的情况。数值实例表明了该方法的有效性。
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引用次数: 0
Structure-preserving joint Lanczos bidiagonalization with thick-restart for the partial quaternion GSVD 针对部分四元数 GSVD 的厚起始保结构联合兰克佐斯对角线化
IF 2.1 3区 数学 Q2 MATHEMATICS, APPLIED Pub Date : 2024-08-01 DOI: 10.1007/s11075-024-01900-1
Zhe-Han Hu, Si-Tao Ling, Zhi-Gang Jia

A new Krylov subspace method is designed in the computation of partial quaternion generalized singular value decomposition (QGSVD) of a large-scale quaternion matrix pair ({textbf{A}, textbf{B}}). Explicitly, we present the structure-preserving joint Lanczos bidiagonalization method to reduce (textbf{A}) and (textbf{B}) to lower and upper real bidiagonal matrices, respectively. We carry out the thick-restarted technique with the combination of a robust selective reorthogonalization strategy in the structure-preserving joint Lanczos bidiagonalization process. In the iteration process we avoid performing the explicit QR decomposition of the quaternion matrix pair. Numerical experiments illustrate the effectiveness of the proposed method.

在计算大规模四元矩阵对({textbf{A}, textbf{B}})的部分四元广义奇异值分解(QGSVD)时,设计了一种新的克雷洛夫子空间方法。明确地说,我们提出了结构保留联合兰克索斯对角线化方法,将 (textbf{A}) 和 (textbf{B}) 分别还原为下实数和上实数对角矩阵。我们在结构保留的联合 Lanczos 二对角化过程中结合稳健的选择性重对角化策略来实现厚起始技术。在迭代过程中,我们避免对四元数矩阵对进行显式 QR 分解。数值实验证明了所提方法的有效性。
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引用次数: 0
期刊
Numerical Algorithms
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