Applied Numerical Mathematics最新文献_第4页

The residual balanced IMEX decomposition for singly-diagonally-implicit schemes

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.030

Savio B. Rodrigues , Giovanni Belloni Fernandes Braga , Marcello Augusto Faraco de Medeiros

{"title":"The residual balanced IMEX decomposition for singly-diagonally-implicit schemes","authors":"Savio B. Rodrigues , Giovanni Belloni Fernandes Braga , Marcello Augusto Faraco de Medeiros","doi":"10.1016/j.apnum.2024.09.030","DOIUrl":"10.1016/j.apnum.2024.09.030","url":null,"abstract":"<div><div>In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable decomposition called residual balanced (RB) decomposition is introduced. This new decomposition maintains time-stepping accuracy even when the implicit equation is only roughly approximated. This novel property is possible because a suitable modification of the traditional IMEX algorithm allows the remaining residual to be seamlessly transferred to the explicit part of the decomposition. The RB decomposition allows an early termination of iterations while preserving time-step accuracy. It can gain computational efficiency by exploring the trade-off between the computational effort placed in the iterative solver and the numerically stable step size. We develop a rigorous theory showing that RB maintains the order of singly diagonally implicit schemes. In computational experiments we show that, in many cases, RB-IMEX reduces the number of iterations when compared with the traditional IMEX method. It is often more stable also. The stability of RB-IMEX is studied using a model containing diffusion and dispersion; in this way, one can visualize how the stability region changes as a function of the number of iterations. Here, computational experiments use ESDIRK schemes for a stiff reaction-advection-diffusion equation, for a Navier-Stokes simulation with acoustic stiffness, and for a semi-implicit implementation of Burguers equation.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 58-78"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097229","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 growth factor of Hadamard matrices of order 20 论 20 阶哈达玛矩阵的增长因子

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.019

Emmanouil Lardas, Marilena Mitrouli

引用次数: 0

The weak Galerkin finite element method for Stokes interface problems with curved interface

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.004

Lin Yang, Qilong Zhai, Ran Zhang

引用次数: 0

An augmented Lagrangian approach for cardinality constrained minimization applied to variable selection problems 应用于变量选择问题的心数受限最小化的增强拉格朗日方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.006

N. Krejić , E.H.M. Krulikovski , M. Raydan

引用次数: 0

On the efficacy of conditioned and progressive Latin hypercube sampling in supervised machine learning 论监督式机器学习中条件式和渐进式拉丁超立方采样的功效

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.016

Ioannis Iordanis, Christos Koukouvinos, Iliana Silou

{"title":"On the efficacy of conditioned and progressive Latin hypercube sampling in supervised machine learning","authors":"Ioannis Iordanis, Christos Koukouvinos, Iliana Silou","doi":"10.1016/j.apnum.2023.12.016","DOIUrl":"10.1016/j.apnum.2023.12.016","url":null,"abstract":"<div><div><span>In this paper, Latin Hypercube Sampling<span> (LHS) method is compared as per its effectiveness in supervised machine learning procedures. Employing LHS saves computer's processing time and in conjunction with Latin hypercube design properties and space filling ability, is considered as one of the most advanced mechanisms in terms of sampling. Although more data usually deliver better results, when using LHS techniques, same quality outputs can be produced with less data and, as a result, </span></span>storage cost<span> and training time are reduced. Conditioned Latin Hypercube Sampling (cLHS) is one of those techniques, successfully performing in supervised machine learning tasks. Unfortunately, the minimum sufficient training dataset size cannot be known in advance. In this case, progressive sampling is recommended since it begins with a small sample and progressively increases its size until model accuracy no longer improves. Combining Latin hypercube sampling and the idea of sequentially incrementing sampling, we test Progressive Latin Hypercube Sampling (PLHS) while monitoring the performance of the sampling-based training as the sample size grows. PLHS and cLHS algorithms are applied in datasets with discrete variables securing that each sample is provided with the Latin hypercube design properties and preserves the principal ability of LHS for space filling, as illustrated in respective sample projecting diagrams. The performance of the above LHS methods in supervised machine learning is evaluated by the degree of training of the model, which is certified through the accuracy of the produced confusion matrices in test files. The results from the use of the above Latin Hypercube Sampling techniques compared against benchmark sampling method empirically prove that machine learning training process becomes less costfull, while remaining reliable.</span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 256-270"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094504","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

Regularisation and iterated regularisation of Hamiltonian systems of the second quasi-Painlevé equation

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.012

Galina Filipuk

引用次数: 0

Penalty hyperparameter optimization with diversity measure for nonnegative low-rank approximation

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.002

Nicoletta Del Buono , Flavia Esposito , Laura Selicato , Rafał Zdunek

{"title":"Penalty hyperparameter optimization with diversity measure for nonnegative low-rank approximation","authors":"Nicoletta Del Buono , Flavia Esposito , Laura Selicato , Rafał Zdunek","doi":"10.1016/j.apnum.2024.10.002","DOIUrl":"10.1016/j.apnum.2024.10.002","url":null,"abstract":"<div><div>Learning tasks are often based on penalized optimization problems in which a sparse solution is desired. This can lead to more interpretative results by identifying a smaller subset of important features or components and reducing the dimensionality of the data representation, as well. In this study, we propose a new method to solve a constrained Frobenius norm-based nonnegative low-rank approximation, and the tuning of the associated penalty hyperparameter, simultaneously. The penalty term added is a particular diversity measure that is more effective for sparseness purposes than other classical norm-based penalties (i.e., <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></span> norms). As it is well known, setting the hyperparameters of an algorithm is not an easy task. Our work drew on developing an optimization method and the corresponding algorithm that simultaneously solves the sparsity-constrained nonnegative approximation problem and optimizes its associated penalty hyperparameters. We test the proposed method by numerical experiments and show its promising results on several synthetic and real datasets.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 189-204"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178962","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

Orthogonal designs for computer experiments constructed from sequences with zero autocorrelation 由零自相关序列构建的计算机实验正交设计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.09.010

Omar A. Alhelali , S.D. Georgiou , C. Koukouvinos , S. Stylianou

引用次数: 0

A new class of symplectic methods for stochastic Hamiltonian systems 随机哈密顿系统的新一类交映法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.021

Cristina Anton

引用次数: 0

Krylov subspace methods for large multidimensional eigenvalue computation 用于大型多维特征值计算的克雷洛夫子空间方法