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ANODE 2023 In honour of John Butcher’s 90th birthday ANODE 2023 纪念约翰-布彻 90 岁生日
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-31 DOI: 10.1007/s11075-024-01849-1
Kevin Burrage, Zdzisław Jackiewicz, Bernd Krauskopf, Yuto Miyatake, Helmut Podhaisky, Mayya Tokman
{"title":"ANODE 2023 In honour of John Butcher’s 90th birthday","authors":"Kevin Burrage, Zdzisław Jackiewicz, Bernd Krauskopf, Yuto Miyatake, Helmut Podhaisky, Mayya Tokman","doi":"10.1007/s11075-024-01849-1","DOIUrl":"https://doi.org/10.1007/s11075-024-01849-1","url":null,"abstract":"","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
C-FISTA type projection algorithm for quasi-variational inequalities 准变不等式的 C-FISTA 型投影算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-30 DOI: 10.1007/s11075-024-01852-6
Yonghong Yao, Lateef O. Jolaoso, Yekini Shehu
{"title":"C-FISTA type projection algorithm for quasi-variational inequalities","authors":"Yonghong Yao, Lateef O. Jolaoso, Yekini Shehu","doi":"10.1007/s11075-024-01852-6","DOIUrl":"https://doi.org/10.1007/s11075-024-01852-6","url":null,"abstract":"<p>In this paper, we first propose a version of FISTA, called C-FISTA type gradient projection algorithm, for quasi-variational inequalities in Hilbert spaces and obtain linear convergence rate. Our results extend the results of Nesterov for C-FISTA algorithm for strongly convex optimization problem and other recent results in the literature where linear convergence results of C-FISTA are obtained for strongly convex composite optimization problems. For a comprehensive study, we also introduce a new version of gradient projection algorithm with momentum terms and give linear rate of convergence. We show the adaptability and effectiveness of our proposed algorithms through numerical comparisons with other related gradient projection algorithms that are in the literature for quasi-variational inequalities.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method 梯度流的两种新型数值方法：不变能量四分法的一般化
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-30 DOI: 10.1007/s11075-024-01847-3
Yukun Yue
{"title":"Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method","authors":"Yukun Yue","doi":"10.1007/s11075-024-01847-3","DOIUrl":"https://doi.org/10.1007/s11075-024-01847-3","url":null,"abstract":"<p>In this paper, we conduct an in-depth investigation of the structural intricacies inherent to the Invariant Energy Quadratization (IEQ) method as applied to gradient flows, and we dissect the mechanisms that enable this method to keep linearity and the conservation of energy simultaneously. Building upon this foundation, we propose two methods: Invariant Energy Convexification and Invariant Energy Functionalization. These approaches can be perceived as natural extensions of the IEQ method. Employing our novel approaches, we reformulate the system connected to gradient flow, construct a semi-discretized numerical scheme, and obtain a commensurate modified energy dissipation law for both proposed methods. Finally, to underscore their practical utility, we provide numerical evidence demonstrating these methods’ accuracy, stability, and effectiveness when applied to both Allen-Cahn and Cahn-Hilliard equations.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Operator-splitting finite element method for solving the radiative transfer equation 用于求解辐射传递方程的算子分裂有限元法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-29 DOI: 10.1007/s11075-024-01850-8
Sashikumaar Ganesan, Maneesh Kumar Singh
{"title":"Operator-splitting finite element method for solving the radiative transfer equation","authors":"Sashikumaar Ganesan, Maneesh Kumar Singh","doi":"10.1007/s11075-024-01850-8","DOIUrl":"https://doi.org/10.1007/s11075-024-01850-8","url":null,"abstract":"<p>An operator-splitting finite element scheme for the time-dependent radiative transfer equation is presented in this paper. The streamline upwind Petrov-Galerkin finite element method and discontinuous Galerkin finite element method are used for the spatial-angular discretization of the radiative transfer equation, whereas the backward Euler scheme is used for temporal discretization. Error analysis of the proposed numerical scheme for the fully discrete radiative transfer equation is presented. The stability and convergence estimates for the fully discrete problem are derived. Moreover, an operator-splitting algorithm for the numerical simulation of high-dimensional equations is also presented. The validity of the derived estimates and implementation is illustrated with suitable numerical experiments.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141173163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction 二维稳态各向异性热传导中的边界重构
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-29 DOI: 10.1007/s11075-024-01831-x
Liviu Marin, Andrei Tiberiu Pantea
{"title":"Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction","authors":"Liviu Marin, Andrei Tiberiu Pantea","doi":"10.1007/s11075-024-01831-x","DOIUrl":"https://doi.org/10.1007/s11075-024-01831-x","url":null,"abstract":"<p>We study the reconstruction of an unknown/inaccessible smooth inner boundary from the knowledge of the Dirichlet condition (temperature) on the entire boundary of a doubly connected domain occupied by a two-dimensional homogeneous anisotropic solid and an additional Neumann condition (normal heat flux) on the known, accessible, and smooth outer boundary in the framework of steady-state heat conduction with heat sources. This inverse geometric problem is approached through an operator that maps an admissible inner boundary belonging to the space of <span>(2pi -)</span>periodic and twice continuously differentiable functions into the Neumann data on the outer boundary which is assumed to be continuous. We prove that this operator is differentiable, and hence, a gradient-based method that employs the anisotropic single layer representation of the solution to an appropriate Dirichlet problem for the two-dimensional anisotropic heat conduction is developed for approximating the unknown inner boundary. Numerical results are presented for both exact and perturbed Neumann data on the outer boundary and show the convergence, stability, and robustness of the proposed method.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Non-blind constraint image deblurring problem with mean curvature functional 具有平均曲率函数的非盲目约束图像去模糊问题
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-24 DOI: 10.1007/s11075-024-01848-2
Ashia Mobeen, Shahbaz Ahmad, Faisal Fairag
{"title":"Non-blind constraint image deblurring problem with mean curvature functional","authors":"Ashia Mobeen, Shahbaz Ahmad, Faisal Fairag","doi":"10.1007/s11075-024-01848-2","DOIUrl":"https://doi.org/10.1007/s11075-024-01848-2","url":null,"abstract":"","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations 一类中性微分方程 Runge-Kutta 方法的延迟稳定性
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-18 DOI: 10.1007/s11075-024-01846-4
Zheng Wang, Yuhao Cong
{"title":"Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations","authors":"Zheng Wang, Yuhao Cong","doi":"10.1007/s11075-024-01846-4","DOIUrl":"https://doi.org/10.1007/s11075-024-01846-4","url":null,"abstract":"<p>In this paper, a class of Runge-Kutta methods for solving neutral delay differential equations (NDDEs) is proposed, which was first introduced by Bassenne et al. (J. Comput. Phys. <b>424</b>, 109847, 2021) for ODEs. In the study, the explicit Runge-Kutta method is multiplied by an operator, which is a Time-Accurate and highly-Stable Explicit operator (TASE-RK), resulting in higher stability than explicit RK. Recently, the multi-parameter TASE-W method was extended by González-Pinto et al. (Appl. Numer. Math. <b>188</b>, 129–145, 2023). We generalized TASE-RK and TASE-W to NDDEs for the first time. Then, by applying the argument principle, sufficient conditions for delay-dependent stability of TASE-RK and TASE-W combined with Lagrange interpolation for NDDEs are investigated. Finally, numerical examples are carried out to verify the theoretical results.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Quantile-based random sparse Kaczmarz for corrupted and noisy linear systems 基于量子的随机稀疏 Kaczmarz，适用于损坏和噪声线性系统
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-13 DOI: 10.1007/s11075-024-01844-6
Lu Zhang, Hongxia Wang, Hui Zhang
{"title":"Quantile-based random sparse Kaczmarz for corrupted and noisy linear systems","authors":"Lu Zhang, Hongxia Wang, Hui Zhang","doi":"10.1007/s11075-024-01844-6","DOIUrl":"https://doi.org/10.1007/s11075-024-01844-6","url":null,"abstract":"<p>The randomized Kaczmarz method, along with its recently developed variants, has become a popular tool for dealing with large-scale linear systems. However, these methods usually fail to converge when the linear systems are affected by heavy corruption, which is common in many practical applications. In this study, we develop a new variant of the randomized sparse Kaczmarz method with linear convergence guarantees, by making use of the quantile technique to detect corruptions. Moreover, we incorporate the averaged block technique into the proposed method to achieve parallel computation and acceleration. Finally, the proposed algorithms are illustrated to be very efficient through extensive numerical experiments.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An Ulm-like algorithm for generalized inverse eigenvalue problems 广义逆特征值问题的类乌尔姆算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-09 DOI: 10.1007/s11075-024-01845-5
Yusong Luo, Weiping Shen
{"title":"An Ulm-like algorithm for generalized inverse eigenvalue problems","authors":"Yusong Luo, Weiping Shen","doi":"10.1007/s11075-024-01845-5","DOIUrl":"https://doi.org/10.1007/s11075-024-01845-5","url":null,"abstract":"<p>In this paper, we study the numerical solutions of the generalized inverse eigenvalue problem (for short, GIEP). Motivated by Ulm’s method for solving general nonlinear equations and the algorithm of Aishima (J. Comput. Appl. Math. <b>367</b>, 112485 2020) for the GIEP, we propose here an Ulm-like algorithm for the GIEP. Compared with other existing methods for the GIEP, the proposed algorithm avoids solving the (approximate) Jacobian equations and so it seems more stable. Assuming that the relative generalized Jacobian matrices at a solution are nonsingular, we prove the quadratic convergence property of the proposed algorithm. Incidentally, we extend the work of Luo et al. (J. Nonlinear Convex Anal. <b>24</b>, 2309–2328 2023) for the inverse eigenvalue problem (for short, IEP) to the GIEP. Some numerical examples are provided and comparisons with other algorithms are made.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Optimality and duality results for fractional programming problems under E-univexity E-univexity 条件下分数程序设计问题的最优性和对偶性结果
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-05-04 DOI: 10.1007/s11075-024-01840-w
S. K. Mishra, D. Singh, Pankaj
{"title":"Optimality and duality results for fractional programming problems under E-univexity","authors":"S. K. Mishra, D. Singh, Pankaj","doi":"10.1007/s11075-024-01840-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01840-w","url":null,"abstract":"<p>In this article, we deal with nonconvex fractional programming problems involving E-differentiable functions <span>((FP_E))</span>. The so-called E-Karush-Kuhn-Tucker sufficient E-optimality conditions are established for nonsmooth optimization problems under E-univexity hypothesis. The established optimality conditions are explained with a numerical example. The so-called vector dual problem in the sense of Schaible <span>((SD_E))</span> involves E-differentiable functions for <span>((FP_E))</span> is defined under E-univexity hypothesis.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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