Journal of Computational and Applied Mathematics最新文献

英文中文

Low-synchronization Arnoldi algorithms with application to exponential integrators 低同步Arnoldi算法及其在指数积分器上的应用

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-11 DOI: 10.1016/j.cam.2026.117342

Tanya V. Tafolla , Stéphane Gaudreault , Mayya Tokman

High order exponential integrators require computing linear combination of exponential-like φ-functions of large matrices A times a vector v. Krylov projection methods are the most general and remain an efficient choice for computing the matrix-function-vector-product evaluation when the matrix A is large and unable to be explicitly stored, or when obtaining information about the spectrum is expensive. The Krylov approximation relies on the Gram-Schmidt (GS) orthogonalization procedure to produce the orthonormal basis V_m. In parallel, GS orthogonalization requires global synchronizations for inner products and vector normalization in the orthogonalization process. Reducing the amount of global synchronizations is of paramount importance for the efficiency of a numerical algorithm in a massively parallel setting. We improve the strong scaling properties and parallel efficiency of exponential integrators by addressing the underlying bottleneck in the linear algebra using low-synchronization GS methods. The resulting orthogonalization algorithms have an accuracy comparable to modified Gram-Schmidt yet are better suited for distributed architecture, as only one global communication is required per orthogonalization-step. We present geophysics based numerical experiments and standard examples routinely used to test stiff time integrators, which validate that reducing global communication leads to better parallel scalability and reduced time-to-solution for exponential integrators.

高阶指数积分器需要计算大矩阵A乘以向量的指数型φ-函数的线性组合。当矩阵A很大且无法显式存储时，或者当获取有关频谱的信息很昂贵时，Krylov投影方法是最通用的，并且仍然是计算矩阵-函数-向量积评估的有效选择。Krylov近似依赖于Gram-Schmidt （GS）正交过程来产生标准正交基Vm。与此同时，GS正交化要求在正交化过程中实现内积和矢量归一化的全局同步。在大规模并行环境下，减少全局同步量对数值算法的效率至关重要。利用低同步GS方法解决了线性代数中的瓶颈问题，提高了指数积分器的强标度特性和并行效率。所得到的正交化算法具有与修改后的Gram-Schmidt相当的精度，但更适合于分布式体系结构，因为每个正交化步骤只需要一次全局通信。我们提出了基于地球物理的数值实验和标准示例，这些实验和标准示例通常用于测试刚性时间积分器，它们验证了减少全球通信可以提高指数积分器的并行可扩展性和缩短求解时间。

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引用次数: 0

A random reshuffling method for generalized Sylvester quaternion matrix equations 广义Sylvester四元数矩阵方程的随机重组方法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.cam.2026.117346

Qiankun Diao , Yiming Jiang , Jinlan Liu , Dongpo Xu

Large-scale quaternion matrix equations face challenges such as high dimensionality and non-commutativity of quaternion multiplication, which often result in high computational complexity and low efficiency with conventional methods. To this end, utilizing generalized Hamilton-real (GHR) calculus, we propose a quaternion random reshuffling (QRR) algorithm for solving large-scale quaternion matrix equations. We also provide a convergence analysis for the QRR algorithm. Numerical experiments show that the QRR algorithm achieves stable convergence performance and faster convergence rates in solving large-scale generalized Sylvester quaternion matrix equations. Thus, the QRR algorithm is expected to provide an efficient and robust solution for solving large-scale quaternion matrix equations.

大规模四元数矩阵方程面临着四元数乘法的高维性和不可交换性等挑战，这往往导致传统方法的计算复杂度高、效率低。为此，我们利用广义Hamilton-real （GHR）演算，提出了求解大规模四元数矩阵方程的四元数随机重组（QRR）算法。我们还提供了QRR算法的收敛性分析。数值实验表明，QRR算法在求解大规模广义Sylvester四元数矩阵方程时具有稳定的收敛性能和较快的收敛速度。因此，QRR算法有望为求解大规模四元数矩阵方程提供高效且鲁棒的解决方案。

引用次数: 0

An inverse random source problem for pseudo-parabolic equation of Caputo type with fractional-order Laplacian operator 具有分数阶拉普拉斯算子的Caputo型伪抛物方程的逆随机源问题

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.cam.2026.117345

Jiamin Lu, Liwen Xu, Hao Cheng

In this paper, we investigate an inverse random source problem for the fractional pseudo-parabolic equation, where the source is driven by a fractional Brownian motion (fBm). For the direct problem, we illustrate the existence and uniqueness of the mild solution. For the inverse random source problem, the uniqueness is proved and the instability is characterized. To address this instability, we apply Tikhonov regularization, achieving stable numerical solutions and giving error estimates. Finally, numerical experiments demonstrate the effectiveness of the regularization method.

本文研究了一类分数阶伪抛物方程的逆随机源问题，其中源是由分数阶布朗运动驱动的。对于直接问题，我们给出了温和解的存在唯一性。对于逆随机源问题，证明了其唯一性，并刻画了其不稳定性。为了解决这种不稳定性，我们应用Tikhonov正则化，获得稳定的数值解并给出误差估计。最后，通过数值实验验证了正则化方法的有效性。

引用次数: 0

Randomized tensor decomposition and optimization in the tucker and tensor train formats 随机张量分解和优化在tucker和张量列格式

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.cam.2026.117344

Wenqi Lu , Hongmei Lin , Heng Lian

Problems involving a low-rank tensor with a Tucker format or a tensor train (TT) format, such as the tensor decomposition or tensor optimization problems, have been frequently studied in the literature. Motivated by the success of randomized algorithms for low-rank matrix decomposition, we develop randomized algorithms for these two tensor formats and present a detailed theoretical analysis of the randomized tensor decomposition as well as on its use in the optimization and regression problem. For the latter, we focus on the nonconvex projected gradient descent algorithm previously used only on the Tucker format, which we also extend to the TT format, where one key step in the computation is performing singular value decomposition of the matricized tensor variable. We provide error bounds both in expectation and bounds with high probability.

涉及具有Tucker格式或张量序列（TT）格式的低秩张量的问题，如张量分解或张量优化问题，在文献中经常被研究。受低秩矩阵分解随机化算法成功的启发，我们针对这两种张量格式开发了随机化算法，并对随机化张量分解及其在优化和回归问题中的应用进行了详细的理论分析。对于后者，我们将重点放在以前仅用于Tucker格式的非凸投影梯度下降算法上，我们也将其扩展到TT格式，其中计算中的一个关键步骤是执行矩阵化张量变量的奇异值分解。我们给出了期望误差和高概率误差的边界。

引用次数: 0

Efficient parallel inversion of ParaOpt preconditioners ParaOpt预条件的高效并行反演

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.cam.2026.117339

Corentin Bonte, Arne Bouillon, Giovanni Samaey, Karl Meerbergen

Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The state-of-the-art parallel preconditioner for linear problems leads to a set of independent smaller systems that are currently hard to solve. We generalize the preconditioner to the nonlinear case and propose a new, fast inversion method for these smaller systems, avoiding disadvantages of the current options with adjusted boundary conditions in the subproblems.

最近，ParaOpt算法被提出，作为时间并行平行法在最优控制中的扩展。ParaOpt使用准牛顿步骤，每个步骤都需要迭代地解决一个匹配条件系统。最先进的线性问题的并行预调节器导致一组独立的小系统，目前难以解决。我们将预条件推广到非线性情况，并针对这些较小的系统提出了一种新的、快速的反演方法，避免了当前具有调整边界条件的子问题方法的缺点。

引用次数: 0

Shape classification of battery cycling profiles via K-Means clustering based on a Sobolev distance 基于Sobolev距离的K-Means聚类电池循环曲线形状分类

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.cam.2026.117365

Maria Grazia Quarta , Ivonne Sgura , Massimo Frittelli , Raquel Barreira , Benedetto Bozzini

Battery cycling, both in application and Research and Development (R&D) environments, generates a wealth of information that often remains underexploited. Thus, potentially valuable information contained in electrical transients is frequently overlooked. In this framework, battery response modelling and model-based data analysis provide powerful tools to extract valuable information on battery status, its evolution and its correlation with functional performance. In this scenario, recently, we have developed a PDE model of battery potential response controlled by electrode shape changes in the BCs for high energy-density metal electrodes. In this work, on the basis of this model, we carry out a classification of the potential transient types, to enable a systematic comparison between model solution and experimental time-series. For transient shape classification purposes, we found that cluster analysis can play a key role in discovering hidden structures within the data. Specifically, in this paper, we apply the K-Means clustering algorithm to classify voltage profiles obtained as numerical solutions of the PDE model for the case of symmetric Li/Li cells. We introduce a weighted discrete Sobolev distance that allows us to spot changes in the shape of the voltage profiles, such as formation of peaks, valleys and concavities, that standard metrics such as the

L^{2}

norm fail to capture. As an application, we consider a selection of experimental galvanostatic discharge-charge potential time-series to classify their shape in terms of cluster centroids. Moreover, we show that the new clustering algorithm can provide a segmentation of the parameter space of the PDE model. This partitioning is useful to link the experimental profiles to specific parameter ranges. In particular, we report an example to validate the fitting results of a recent publication of ours obtained via a Deep Learning approach for the same measured profiles.

无论是在应用还是研发环境中，电池循环都会产生大量的信息，而这些信息往往尚未得到充分利用。因此，电瞬变中包含的潜在有价值的信息经常被忽视。在此框架下，电池响应建模和基于模型的数据分析为提取电池状态、演变及其与功能性能的相关性提供了强大的工具。在这种情况下，最近，我们开发了一个PDE模型，用于高能量密度金属电极，该模型由bc中电极形状变化控制电池电位响应。在这项工作中，我们在该模型的基础上，对潜在瞬态类型进行了分类，以便将模型解与实验时间序列进行系统比较。对于瞬态形状分类，我们发现聚类分析可以在发现数据中的隐藏结构方面发挥关键作用。具体而言，在本文中，我们应用K-Means聚类算法对对称Li/Li电池的PDE模型的数值解得到的电压分布进行分类。我们引入了一个加权的离散Sobolev距离，使我们能够发现电压分布形状的变化，例如峰、谷和凹的形成，这些都是L2范数等标准度量无法捕捉到的。作为一种应用，我们考虑选择实验恒流放电-电荷电位时间序列，根据簇质心对它们的形状进行分类。此外，我们还证明了新的聚类算法可以对PDE模型的参数空间进行分割。这种划分有助于将实验配置文件链接到特定的参数范围。特别地，我们报告了一个例子来验证我们最近通过深度学习方法获得的相同测量剖面的拟合结果。

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引用次数: 0

Behavior of a nonlocal species-pathogen system with varied dispersal mechanisms in heterogeneous habitats 异质生境中具有不同扩散机制的非本地物种-病原体系统的行为

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.cam.2026.117341

Boumdiene Guenad , Salih Djilali , Soufiane Bentout

This research is about a nonlocal dispersal host-pathogen model with Neumann boundary conditions. The nonlocal dispersion operator lacks compactness, which generates an additional challenge in showing the existence of a global compact attractor, and then the stability of the steady states. Therefore, we study the asymptotic stability of the positive steady states, where we show that depends on R₀. For R₀ < 1, we prove the global asymptotic stability of the pathogen-free steady state, whereas for R₀ > 1, we demonstrate the model’s uniform persistence and the existence of a positive steady state. Moreover, we establish the global behavior of the positive steady state for two cases: (i) the spatially homogeneous case, with both dispersal coefficients are not a zero, (ii) the spatially heterogeneous case, with one of the dispersion rate is a zero. Finally, the asymptotic profiles of the positive steady state as one or both diffusion coefficients tend to infinity is established. This gives the most favored sites for the host and virus particles. Our results shed light on the interplay between spatial dispersal and disease dynamics and have implications for the design of effective control strategies.

本文研究了具有诺伊曼边界条件的非局部传播宿主-病原体模型。非局部色散算子缺乏紧致性，这给证明全局紧致吸引子的存在性以及稳态的稳定性带来了额外的挑战。因此，我们研究了正稳态的渐近稳定性，其中我们证明了它依赖于R0。对于R0 <； 1，我们证明了无病原体稳态的全局渐近稳定性，而对于R0 >； 1，我们证明了模型的均匀持续性和正稳态的存在性。此外，我们建立了两种情况下的全局正稳态行为：(i)空间均匀情况下，两个扩散系数都不为零，（ii）空间非均匀情况下，其中一个扩散率为零。最后，建立了一个或两个扩散系数趋于无穷大时正稳态的渐近曲线。这为宿主和病毒粒子提供了最有利的位置。我们的研究结果揭示了空间扩散与疾病动态之间的相互作用，并对设计有效的控制策略具有启示意义。

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引用次数: 0

Combinatorial and recurrent approaches for efficient matrix inversion: Sub-cubic algorithms leveraging fast matrix products 有效矩阵反演的组合和循环方法：利用快速矩阵乘积的次立方算法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.cam.2026.117351

Mohamed Kamel RIAHI

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and a recurrent formalism, incorporating Strassen’s fast matrix multiplication algorithm. Our focus lies on triangular matrices, where we propose a unique computational approach based on combinatorial techniques for directly inverting general non-singular triangular matrices. Unlike iterative methods, our combinatorial approach enables the direct construction of the inverse through nonlinear combinations of carefully selected matrix entries, allowing full parallelization and efficient implementation on parallel architectures. Although combinatorial algorithms often suffer from exponential time complexity, limiting their practical use, our method overcomes this by deriving recurrent relations that facilitate recursive triangular splitting, striking a balance between efficiency and accuracy. We provide rigorous mathematical proofs to validate the approach and present extensive numerical experiments demonstrating its effectiveness.

Additionally, we develop several innovative numerical linear algebra algorithms that directly factorize the inverse of general matrices, with significant potential for generating preconditioners that accelerate Krylov subspace iterative solvers and improve the solution of large-scale linear systems.

Our comprehensive evaluation confirms that the proposed algorithms outperform classical approaches in terms of computational efficiency, opening up new avenues for advanced matrix inversion techniques and the development of effective preconditioning strategies.

在本文中，我们引入了新的快速矩阵反演算法，利用三角分解和循环形式，结合Strassen的快速矩阵乘法算法。我们的重点在于三角矩阵，在那里我们提出了一个独特的计算方法，基于组合技术直接反演一般的非奇异三角矩阵。与迭代方法不同，我们的组合方法可以通过精心选择的矩阵项的非线性组合直接构造逆，从而允许在并行架构上实现完全并行化和高效实现。虽然组合算法经常遭受指数时间复杂度的困扰，限制了它们的实际应用，但我们的方法通过推导递归关系来克服这个问题，从而促进递归三角分裂，在效率和准确性之间取得平衡。我们提供了严格的数学证明来验证该方法，并提供了大量的数值实验来证明其有效性。此外，我们开发了几个创新的数值线性代数算法，直接分解一般矩阵的逆，具有显著的潜力生成预条件，加速Krylov子空间迭代求解和改进大规模线性系统的解决方案。我们的综合评估证实，所提出的算法在计算效率方面优于经典方法，为先进的矩阵反演技术和有效预处理策略的开发开辟了新的途径。

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引用次数: 0

Pricing vulnerable extremum options in a Markov regime-switching Heston’s model and stochastic interest rate 马尔可夫状态下易损极值期权的定价——交换赫斯顿模型和随机利率

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.cam.2025.117332

Guohe Deng, Yurong Xie

Pricing options on the maximum or the minimum of several underlying assets (called extremum options) has always been one of the key problems in financial engineering because of high dimensionality. In this paper, we consider the pricing problem of European-style vulnerable extremum options under the Heston model and stochastic interest rate model in which the mean-reversion levels of both variance and interest rate processes are modulated by a continuous-time Markov chain with finite states. Integral representations for the pricing formulas of the vulnerable extremum options are derived by using the Esscher transform, joint characteristic function and multivariate Fourier transform technique. Then we provide the efficient approximation to calculate the semi-analytical pricing formulas of this option using the modified discrete fast Fourier transform (FFT) approach and examine the accuracy of the approximation by Monte Carlo simulation. Finally, numerical results for the prices or (and) its Delta values of the vulnerable extremum call options arising in the proposed model are given in a two-regime case. Further, the effect of introducing regime-switching into both the Heston model and stochastic interest rate model is investigated, and the sensitivity analysis of different parameters in this model on the option price are provided. Numerical experiments are provided to illustrate the significance of regime-switching risk in option pricing.

基于若干标的资产的最大值或最小值的期权定价（称为极值期权）由于其高维性一直是金融工程中的关键问题之一。本文研究了在随机利率模型和Heston模型下欧式易损极值期权的定价问题，其中方差过程和利率过程的均值回归水平均由有限状态的连续马尔可夫链调制。利用Esscher变换、联合特征函数和多元傅里叶变换技术，导出了脆弱极值期权定价公式的积分表示。然后利用改进的离散快速傅里叶变换（FFT）方法给出了该期权半解析定价公式的有效逼近，并通过蒙特卡罗模拟检验了逼近的准确性。最后，给出了在两种情形下模型中产生的脆弱极值看涨期权的价格或（和）其Delta值的数值结果。进一步研究了在赫斯顿模型和随机利率模型中引入制度转换的影响，并对该模型中不同参数对期权价格的敏感性进行了分析。通过数值实验说明了制度转换风险在期权定价中的重要性。

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An ADI scheme for convection diffusion equation with variable coefficients on irregular domain 不规则区域上变系数对流扩散方程的ADI格式

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2026-01-06 DOI: 10.1016/j.cam.2026.117350

Xue-Lei Lin , Chengyu Chen , Ye Liu , Huifang Yuan

The alternating direction implicit (ADI) scheme is a type of well-known fast solvable scheme, which is frequently studied for time-dependent problems with constant coefficients on rectangular domains. Due to the complicated algebraic matrix structure, it is rare to study the ADI schemes for time-dependent problems with variable coefficients on irregular domains in the literature. In this paper, we study a novel ADI scheme for the well-known challenging problem: convection-dominated convection diffusion equation with variable coefficients on two-dimensional irregular domain. An upwind difference scheme is proposed for the spatial discretization, which leads to diagonally dominant spatial discretization matrices. The ADI temporal discretization reduces the two-dimension spatial problem into two one-dimension spatial sub-problems, in which the sub-problem along x-direction has a tridiagonal structure while the sub-problem along y-direction is sparse and unstructured due to the complicated domain geometry. To handle the complicated structure of the y-sub-problems, a grid adaptive permutation technique is proposed to convert the y-sub-problems into tridiagonal systems. As a result, all the one-dimension sub-problems arising from the proposed ADI schemes are diagonally dominant tridiagonal systems, which can be fast and directly solved by banded LU factorization with optimal complexity (i.e., linear complexity). It is well-known that the complicated domain geometry and the dominance of the convection terms bring challenge to numerical solution of the equation. Remarkably, both theoretical results and numerical results show that the proposed scheme is unconditionally stable with respect to the dominance of the convection term, time-space grid ratio and is flexible to the domain geometry.

交替方向隐式（ADI）格式是一种众所周知的快速可解格式，常用于矩形域上常系数时变问题的研究。由于代数矩阵结构复杂，对不规则域上变系数时变问题的ADI格式研究较少。本文研究了二维不规则区域上以对流为主的变系数对流扩散方程的一种新颖的ADI格式。提出了一种空间离散化的迎风差分格式，从而得到对角占优的空间离散化矩阵。ADI时间离散化将二维空间问题分解为两个一维空间子问题，其中沿x方向的子问题具有三对角结构，而沿y方向的子问题由于复杂的域几何结构而稀疏且非结构化。针对y子问题的复杂结构，提出了一种网格自适应置换技术，将y子问题转化为三对角系统。结果表明，所提出的ADI方案所产生的一维子问题都是对角占优的三对角系统，可以用最优复杂度（即线性复杂度）的带状LU分解快速直接求解。众所周知，复杂的区域几何和对流项的优势给方程的数值求解带来了挑战。理论结果和数值结果均表明，该格式在对流项、时空网格比的主导地位方面是无条件稳定的，并且对区域几何结构具有灵活性。

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