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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
Numerical Algorithms Pub Date : 2024-08-05 DOI: 10.1007/s11075-024-01892-y
Ziheng Chen, Liangmin Cao, Lin Chen
{"title":"Stochastic theta methods for random periodic solution of stochastic differential equations under non-globally Lipschitz conditions","authors":"Ziheng Chen, Liangmin Cao, Lin Chen","doi":"10.1007/s11075-024-01892-y","DOIUrl":"https://doi.org/10.1007/s11075-024-01892-y","url":null,"abstract":"<p>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 <span>(theta in (1/2,1])</span>. 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.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935557","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
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
Numerical Algorithms Pub Date : 2024-08-02 DOI: 10.1007/s11075-024-01899-5
Peizhao Yu, Fuheng Zhao, Haoming Xin
{"title":"Optimization algorithms for stabilization of multi-input vibration system with time delay using eigenvalues assignment technique","authors":"Peizhao Yu, Fuheng Zhao, Haoming Xin","doi":"10.1007/s11075-024-01899-5","DOIUrl":"https://doi.org/10.1007/s11075-024-01899-5","url":null,"abstract":"<p>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.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881205","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
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
Numerical Algorithms Pub Date : 2024-08-01 DOI: 10.1007/s11075-024-01900-1
Zhe-Han Hu, Si-Tao Ling, Zhi-Gang Jia
{"title":"Structure-preserving joint Lanczos bidiagonalization with thick-restart for the partial quaternion GSVD","authors":"Zhe-Han Hu, Si-Tao Ling, Zhi-Gang Jia","doi":"10.1007/s11075-024-01900-1","DOIUrl":"https://doi.org/10.1007/s11075-024-01900-1","url":null,"abstract":"<p>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 <span>({textbf{A}, textbf{B}})</span>. Explicitly, we present the structure-preserving joint Lanczos bidiagonalization method to reduce <span>(textbf{A})</span> and <span>(textbf{B})</span> 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.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870103","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
Variable parameter Uzawa method for solving the indefinite least squares problem 求解不定最小二乘法问题的可变参数乌泽法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-31 DOI: 10.1007/s11075-024-01905-w
Lingsheng Meng, Kailiang Xin, Jun Li
{"title":"Variable parameter Uzawa method for solving the indefinite least squares problem","authors":"Lingsheng Meng, Kailiang Xin, Jun Li","doi":"10.1007/s11075-024-01905-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01905-w","url":null,"abstract":"<p>In this paper, the variable parameter Uzawa method is presented to solve the indefinite least squares problem. The proposed iterative method is unconditionally convergent, and its iterative algorithm and parameter designing are simple and efficient. Numerical experiments show that the variable parameter Uzawa method is superior to the USSOR method (Song, Int. J. Comput. Math. <b>97</b>, 1781–1791 2020) and the splitting-based randomized iterative method (Zhang and Li, Appl. Math. Comput. <b>446</b>, 127892 2023).</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870101","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
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair 计算大型正则矩阵对的多个 GSVD 分量的改进和改进谐波雅各比-戴维森方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-31 DOI: 10.1007/s11075-024-01901-0
Jinzhi Huang, Zhongxiao Jia
{"title":"Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair","authors":"Jinzhi Huang, Zhongxiao Jia","doi":"10.1007/s11075-024-01901-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01901-0","url":null,"abstract":"<p>Three refined and refined harmonic extraction-based Jacobi–Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition (GSVD) components of a large regular matrix pair. The new methods are called refined cross product-free (RCPF), refined cross product-free harmonic (RCPF-harmonic) and refined inverse-free harmonic (RIF-harmonic) JDGSVD algorithms, abbreviated as RCPF-JDGSVD, RCPF-HJDGSVD and RIF-HJDGSVD, respectively. The new JDGSVD methods are more efficient than the corresponding standard and harmonic extraction-based JDSVD methods proposed previously by the authors, and can overcome the erratic behavior and intrinsic possible non-convergence of the latter ones. Numerical experiments illustrate that RCPF-JDGSVD performs better for the computation of extreme GSVD components while RCPF-HJDGSVD and RIF-HJDGSVD are more suitable for that of interior GSVD components.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873268","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
A Tikhonov-type regularization method for Caputo fractional derivative 卡普托分数导数的提霍诺夫式正则化方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-30 DOI: 10.1007/s11075-024-01883-z
Nguyen Van Duc, Thi-Phong Nguyen, Nguyen Phuong Ha, Nguyen The Anh, Luu Duc Manh, Hoang Cong Gia Bao
{"title":"A Tikhonov-type regularization method for Caputo fractional derivative","authors":"Nguyen Van Duc, Thi-Phong Nguyen, Nguyen Phuong Ha, Nguyen The Anh, Luu Duc Manh, Hoang Cong Gia Bao","doi":"10.1007/s11075-024-01883-z","DOIUrl":"https://doi.org/10.1007/s11075-024-01883-z","url":null,"abstract":"<p>Stability estimates of Hölder type for the problem of evaluating the Caputo fractional derivative are obtained. This ill-posed problem is regularized by a Tikhonov-type method, which guarantees error estimates of Hölder type. Numerical results are presented to confirm the theory.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870100","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
Generalized weak Galerkin finite element method for linear elasticity interface problems 线性弹性界面问题的广义弱 Galerkin 有限元方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-29 DOI: 10.1007/s11075-024-01904-x
Yue Wang, Fuzheng Gao
{"title":"Generalized weak Galerkin finite element method for linear elasticity interface problems","authors":"Yue Wang, Fuzheng Gao","doi":"10.1007/s11075-024-01904-x","DOIUrl":"https://doi.org/10.1007/s11075-024-01904-x","url":null,"abstract":"<p>A generalized weak Galerkin finite element method for linear elasticity interface problems is presented. The generalized weak gradient (divergence) is consisted of classical gradient (divergence) and the solution of local problem. Thus, the finite element space can be extended to arbitrary combination of piecewise polynomial spaces. The error equation and error estimates are proved. The numerical results illustrate the efficiency and flexibility for different interfaces, partitions and combinations, the locking-free property, the well performance for low regularity solution in discrete energy, <span>(L^2)</span> and <span>(L^{infty })</span> norms. Meanwhile, we present the numerical comparison between our algorithm and the weak Galerkin finite element algorithm to demonstrate the flexibility of our algorithm. In addition, for some cases, the convergence rates in numerical tests are obviously higher than the theoretical prediction for the smooth and low regularity solutions.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870102","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
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems 一般二阶振荡系统的扩展显式伪两步 Runge-Kutta-Nyström 方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-29 DOI: 10.1007/s11075-024-01896-8
Yonglei Fang, Changying Liu, Xiong You
{"title":"Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems","authors":"Yonglei Fang, Changying Liu, Xiong You","doi":"10.1007/s11075-024-01896-8","DOIUrl":"https://doi.org/10.1007/s11075-024-01896-8","url":null,"abstract":"<p>Explicit pseudo two-step extended Runge-Kutta-Nyström (EPTSERKN) methods for the numerical integration of general second-order oscillatory differential systems are discussed in this paper. New explicit pseudo two-step Runge-Kutta-Nyström (EPTSRKN) methods and explicit extended Runge-Kutta-Nyström (ERKN) methods are derived. We give the global error analysis of the new methods. The <i>s</i>-stages new methods are of order <span>(s+1)</span> with some suitable nodes. Numerical experiments are carried out to show the efficiency and robustness of the new methods.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870104","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
Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations 求解随机伊托-伏特拉积分方程的快速准确数值算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-29 DOI: 10.1007/s11075-024-01898-6
Rebiha Zeghdane
{"title":"Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations","authors":"Rebiha Zeghdane","doi":"10.1007/s11075-024-01898-6","DOIUrl":"https://doi.org/10.1007/s11075-024-01898-6","url":null,"abstract":"<p>The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870112","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
Limited memory gradient methods for unconstrained optimization 无约束优化的有限记忆梯度法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-26 DOI: 10.1007/s11075-024-01895-9
Giulia Ferrandi, Michiel E. Hochstenbach
{"title":"Limited memory gradient methods for unconstrained optimization","authors":"Giulia Ferrandi, Michiel E. Hochstenbach","doi":"10.1007/s11075-024-01895-9","DOIUrl":"https://doi.org/10.1007/s11075-024-01895-9","url":null,"abstract":"<p>The limited memory steepest descent method (LMSD, Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review this method and propose new variants. For strictly convex quadratic objective functions, we study the numerical behavior of different techniques to compute new stepsizes. In particular, we introduce a method to improve the use of harmonic Ritz values. We also show the existence of a secant condition associated with LMSD, where the approximating Hessian is projected onto a low-dimensional space. In the general nonlinear case, we propose two new alternatives to Fletcher’s method: first, the addition of symmetry constraints to the secant condition valid for the quadratic case; second, a perturbation of the last differences between consecutive gradients, to satisfy multiple secant equations simultaneously. We show that Fletcher’s method can also be interpreted from this viewpoint.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785244","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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