Applied Numerical Mathematics最新文献

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Central composite designs with three missing observations 有三个缺失观测点的中心复合设计

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.013

K. Alanazi , S.D. Georgiou , C. Koukouvinos , S. Stylianou

In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. This work therefore investigates the impact of a three missing observation of them various design points: factorial, axial and center points, on the estimation and predictive capability of the central composite design (CCD). Therefore minimaxloss CCD is formulated under a minimaxloss criterion. The minimaxloss CCD is considered to be robust to three missing observation and the investigation has been made in this article. The general formulas for the efficiency of the design when missing three observations, are presented in closed form as a function of α, where α is the value used in the CCDs' axial part. For the first time in this paper, these are calculated explicitly for CCDs from

k = 2

k = 7

factors and displayed in tables for practitioners to use. The corresponding graphs for the efficiencies are presented and suggestions are made for the values of α to maximize the robustness and estimability of the design for all cases.

在实验中，由于一些意外事故或高成本实验，有很多情况下会遗漏、忽略或无法获得某些观测数据。观测数据的缺失会使响应面模型的结果产生误导。因此，这项工作研究了不同设计点（因子点、轴向点和中心点）的三个观测点缺失对中心复合设计（CCD）的估计和预测能力的影响。因此，最小损失 CCD 是在最小损失准则下制定的。本文认为最小损失 CCD 对三个缺失观测点具有鲁棒性，并对其进行了研究。本文以闭合形式给出了缺失三个观测点时设计效率的一般公式，作为 α 的函数，其中 α 是 CCD 轴向部分使用的值。本文首次明确计算了从 k=2 到 k=7 因子的 CCD 的效率，并以表格形式显示，供从业人员使用。本文还给出了相应的效率图表，并对 α 值提出了建议，以最大限度地提高所有情况下设计的稳健性和可估算性。

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引用次数: 0

A priori and a posteriori error estimates for efficient numerical schemes for coupled systems of linear and nonlinear singularly perturbed initial-value problems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.005

Carmelo Clavero , Shashikant Kumar , Sunil Kumar

This work considers the numerical approximation of linear and nonlinear singularly perturbed initial value coupled systems of first-order, for which the diffusion parameters at each equation of the system are distinct and also they can have a different order of magnitude. To do that, we use two efficient discretization methods, which combine the backward differences and an appropriate splitting by components. Both a priori and a posteriori error estimates are proved for the proposed discretization methods. The developed numerical methods are more computationally efficient than those classical methods used to solve the same type of coupled systems. Extensive numerical experiments strongly confirm in practice the theoretical results and corroborate the superior performance of the current approach compared with previous existing approaches.

引用次数: 0

Multilinear algebra methods for higher-dimensional graphs 高维图的多重线性代数方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.11.009

Alaeddine Zahir , Khalide Jbilou , Ahmed Ratnani

In this paper, we will explore the use of multilinear algebra-based methods for higher dimensional graphs. Multi-view clustering (MVC) has gained popularity over the single-view clustering due to its ability to provide more comprehensive insights into the data. However, this approach also presents challenges, particularly in combining and utilizing multiple views or features effectively. Most of recent work in this field focuses mainly on tensor representation instead of treating the data as simple matrices. Accordingly, we will examine and compare these approaches, particularly in two categories, namely graph-based clustering and subspace-based clustering. We will report on experiments conducted using benchmark datasets to evaluate the performance of the main clustering methods.

在本文中，我们将探讨使用基于多线性代数的方法来处理高维图。多视图集群(MVC)比单视图集群更受欢迎，因为它能够提供更全面的数据洞察。然而，这种方法也提出了挑战，特别是在有效地组合和利用多个视图或特性方面。该领域最近的大部分工作主要集中在张量表示上，而不是将数据视为简单的矩阵。因此，我们将检查和比较这些方法，特别是在两个类别中，即基于图的聚类和基于子空间的聚类。我们将报告使用基准数据集进行的实验，以评估主要聚类方法的性能。

引用次数: 0

Weighted chained graphs and some applications 加权链图和一些应用

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.017

C. Fenu , L. Reichel , G. Rodriguez , Y. Zhang

This paper introduces weighted chained graphs, as well as minimal broadcasting and receiving sets, and investigates their properties. Both directed and undirected graphs are considered. The notion of central nodes is introduced both for weighted directed and undirected graphs. This notion is helpful for determining how quickly information can propagate throughout a graph. In particular, it is useful for the investigation of transportation networks and for city planning. Applications to the analysis of airline and bus networks are presented.

本文介绍了加权链图以及最小广播集和接收集，并研究了它们的特性。本文考虑了有向图和无向图。在有向和无向图中都引入了中心节点的概念。这一概念有助于确定信息在整个图中传播的速度。特别是，它对研究交通网络和城市规划非常有用。本文介绍了中心节点在航空和公共汽车网络分析中的应用。

引用次数: 0

A Multi-Quadrics quasi-interpolation scheme for numerical solution of Burgers' equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.025

JiHong Zhang, JiaLi Yu

The Multi-Quadrics (MQ) radial basis function (RBF) quasi-interpolant has received widespread attention due to its simplicity and convenience, avoiding the possible ill-conditioning problem that may occur if there are a lot of interpolation points, and being able to directly provide numerical approximation results. We present a new quasi-interpolant

L_{N}

for scattered data and prove that it has the property of linear reproducing and high computational accuracy, and does not require the first derivative values at the two endpoints, making it easier to use. Finally, the numerical scheme for solving Burgers’ equation is presented, and numerical experiments are carried out and compared with other methods. The numerical results verify the effectiveness and accuracy of the new quasi-interpolant

L_{N}

引用次数: 0

On an algorithm for the numerical solution of quasilinear integral-algebraic equations

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.008

Mikhail Bulatov , Tatiana Indutskaya , Liubov Solovarova

This article addresses interrelated integral nonlinear Volterra equations of the first and second kinds. Combining them, we obtain a system of integral equations with an identically degenerate matrix multiplying by the main part, which is usually called integral-algebraic equations. We highlight the fundamental features of the problems under consideration, namely their ill-posedness. We give conditions for the existence of a unique sufficiently smooth solution in terms of matrix pencils and propose an algorithm for their numerical solution, which is based on the simplest quadrature formula and linearization of a nonlinear integrand. Illustrative examples and results of numerical calculations of test examples are given.

引用次数: 0

Numerical differentiation of the piecewise smooth function by using Fourier extension method

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.026

Zhenyu Zhao , Kai Yu , Xianzheng Jia , Zhihong Dou

Numerical differentiation of the piecewise smooth function is considered in this paper. To avoid the large error of numerical differentiation that may occur near potential non-smooth points, we identify the discontinuity points of the first or second derivative of the function. Then we divide the domain of the function into several sub-domains. For each sub-domain, the approximation is constructed by Fourier extension, and the global approximation of the piecewise smooth function is formed by superposition to improve accuracy. Some numerical experiments are conducted to further verify the efficacy of the method.

引用次数: 0

An explicit substructuring method for overlapping domain decomposition based on stochastic calculus 基于随机微积分的重叠域分解显式子结构方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.02.011

Jorge Morón-Vidal, Francisco Bernal, Atsushi Suzuki

In a recent paper [7], a hybrid supercomputing algorithm for elliptic equations has been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques, such as the Schur complement method for the skeleton, the hybrid approach produces an explicit and sparse shrunken matrix—hence suitable for substructuring again. The ultimate goal is to push strong scalability beyond the state of the art by leveraging the potential for parallelisation of stochastic calculus. Here, we present a major revamping of that framework, based on the insight of embedding the domain in a cover of overlapping circles (in two dimensions). This allows for efficient Fourier interpolation along the interfaces (now circumferences) and—crucially—for the evaluation of most of the interfacial system entries as the solution of small boundary value problems on a circle. This is both extremely efficient (as they can be solved in parallel and by the pseudospectral method) and free of Monte Carlo error. Stochastic numerics are only needed on the relatively few circles intersecting the domain boundary. In sum, the new formulation is significantly faster, simpler, and more accurate while retaining all of the advantageous properties of PDDSparse. Numerical experiments are included for the purpose of illustration.

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引用次数: 0

The Crank-Nicolson weak Galerkin finite element methods for the sine-Gordon equation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-01-29 DOI: 10.1016/j.apnum.2025.01.016

Ahmed Al-Taweel , Jumana Alkhalissi , Xiaoshen Wang

This article proposes an efficient second-order weak Galerkin (WG) finite element scheme for solving the 2D damped and undamped sine-Gordon problem with Dirichlet boundary conditions and initial conditions. We also construct and study a fully discrete WG finite element method for solving the sine-Gordon equation with a damping term using the Crank–Nicolson (CN) and Euler schemes. Stability and error analyses are established on a triangular grid for the constructed schemes in

L^{2}

and

H^{1}

norms for the fully discrete and semi-discrete formulation. Our formulation is accurate in space and time. Finally, numerical experiments are performed to validate the theoretical conclusions.

引用次数: 0

Spectral element method for the solution of viscoelastic seismic wave propagation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2025-01-27 DOI: 10.1016/j.apnum.2025.01.015

Feze Barzegar, Jalil Rashidinia

This paper considers the Gauss–Legendre–Lobatto spectral element method combined with the Crank–Nicolson (CN) technique to solve the viscoelastic wave equation model. The CN technique is chosen for its unconditional stability and second-order accuracy. Additionally, the convergence order is determined for the time semi-discrete scheme of the problem. The Gauss–Legendre–Lobatto points are used as interpolation nodes and integral quadrature points to discretize the spatial direction with the spectral element method, providing an a priori estimate. Numerical results demonstrate the proposed method's high efficiency and accuracy.

引用次数: 0

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