Advances in Computational Mathematics最新文献_第6页

Balanced truncation for quadratic-bilinear control systems 二次线性控制系统的平衡截断

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-08-08 DOI: 10.1007/s10444-024-10186-9

Peter Benner, Pawan Goyal

{"title":"Balanced truncation for quadratic-bilinear control systems","authors":"Peter Benner, Pawan Goyal","doi":"10.1007/s10444-024-10186-9","DOIUrl":"10.1007/s10444-024-10186-9","url":null,"abstract":"<div><p>We discuss model order reduction (MOR) for large-scale quadratic-bilinear (QB) systems based on balanced truncation. The method for linear systems mainly involves the computation of the Gramians of the system, namely reachability and observability Gramians. These Gramians are extended to a general nonlinear setting in Scherpen (Systems Control Lett. <b>21</b>, 143-153 1993). These formulations of Gramians are not only challenging to compute for large-scale systems but hard to utilize also in the MOR framework. This work proposes algebraic Gramians for QB systems based on the underlying Volterra series representation of QB systems and their Hilbert adjoint systems. We then show their relation to a certain type of generalized quadratic Lyapunov equation. Furthermore, we quantify the reachability and observability subspaces based on the proposed Gramians. Consequently, we propose a balancing algorithm, allowing us to find those states that are simultaneously hard to reach and hard to observe. Truncating such states yields reduced-order systems. We also study sufficient conditions for the existence of Gramians, and a local stability of reduced-order models obtained using the proposed balanced truncation scheme. Finally, we demonstrate the proposed balancing-type MOR for QB systems using various numerical examples.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10186-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141904535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data 非光滑数据的后向分数费曼-卡克方程的 WSGD 方案分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-08-08 DOI: 10.1007/s10444-024-10188-7

Liyao Hao, Wenyi Tian

引用次数: 0

Weights for moments’ geometrical localization: a canonical isomorphism 力矩几何定位的权重：典型同构

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-08-06 DOI: 10.1007/s10444-024-10183-y

Ana Alonso Rodríguez, Jessika Camaño, Eduardo De Los Santos, Francesca Rapetti

引用次数: 0

Online identification and control of PDEs via reinforcement learning methods 通过强化学习方法对 PDE 进行在线识别和控制

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-08-01 DOI: 10.1007/s10444-024-10167-y

Alessandro Alla, Agnese Pacifico, Michele Palladino, Andrea Pesare

引用次数: 0

Averaging property of wedge product and naturality in discrete exterior calculus 离散外部微积分中的楔积平均特性和自然性

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-31 DOI: 10.1007/s10444-024-10179-8

Mark D. Schubel, Daniel Berwick-Evans, Anil N. Hirani

引用次数: 0

Two-grid stabilized finite element methods with backtracking for the stationary Navier-Stokes equations 静态纳维-斯托克斯方程的双网格稳定有限元法与回溯法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-30 DOI: 10.1007/s10444-024-10180-1

Jing Han, Guangzhi Du

引用次数: 0

Analysis of the leapfrog-Verlet method applied to the Kuwabara-Kono force model in discrete element method simulations of granular materials 粒状材料离散元法模拟中库瓦巴拉-科诺力模型的跃迁-韦勒法应用分析

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-23 DOI: 10.1007/s10444-024-10162-3

Gabriel Nóbrega Bufolo, Yuri Dumaresq Sobral

引用次数: 0

Randomized greedy magic point selection schemes for nonlinear model reduction 用于非线性模型还原的随机贪婪魔法点选择方案

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-22 DOI: 10.1007/s10444-024-10172-1

Ralf Zimmermann, Kai Cheng

{"title":"Randomized greedy magic point selection schemes for nonlinear model reduction","authors":"Ralf Zimmermann, Kai Cheng","doi":"10.1007/s10444-024-10172-1","DOIUrl":"10.1007/s10444-024-10172-1","url":null,"abstract":"<div><p>An established way to tackle model nonlinearities in projection-based model reduction is via relying on partial information. This idea is shared by the methods of gappy proper orthogonal decomposition (POD), missing point estimation (MPE), masked projection, hyper reduction, and the (discrete) empirical interpolation method (DEIM). The selected indices of the partial information components are often referred to as “magic points.” The original contribution of the work at hand is a novel randomized greedy magic point selection. It is known that the greedy method is associated with minimizing the norm of an oblique projection operator, which, in turn, is associated with solving a sequence of rank-one SVD update problems. We propose simplification measures so that the resulting greedy point selection has the following main features: (1) The inherent rank-one SVD update problem is tackled in a way, such that its dimension does not grow with the number of selected magic points. (2) The approach is online efficient in the sense that the computational costs are independent from the dimension of the full-scale model. To the best of our knowledge, this is the first greedy magic point selection that features this property. We illustrate the findings by means of numerical examples. We find that the computational cost of the proposed method is orders of magnitude lower than that of its deterministic counterpart. Nevertheless, the prediction accuracy is just as good if not better. When compared to a state-of-the-art randomized method based on leverage scores, the randomized greedy method outperforms its competitor.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10172-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

The (L_q)-weighted dual programming of the linear Chebyshev approximation and an interior-point method 线性切比雪夫近似的 $$L_q$$ 加权对偶编程和一种内点法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-22 DOI: 10.1007/s10444-024-10177-w

Yang Linyi, Zhang Lei-Hong, Zhang Ya-Nan

引用次数: 0

On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems 关于偏斜对称和移位偏斜对称线性系统的克雷洛夫子空间方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2024-07-19 DOI: 10.1007/s10444-024-10178-9

Kui Du, Jia-Jun Fan, Xiao-Hui Sun, Fang Wang, Ya-Lan Zhang

{"title":"On Krylov subspace methods for skew-symmetric and shifted skew-symmetric linear systems","authors":"Kui Du, Jia-Jun Fan, Xiao-Hui Sun, Fang Wang, Ya-Lan Zhang","doi":"10.1007/s10444-024-10178-9","DOIUrl":"10.1007/s10444-024-10178-9","url":null,"abstract":"<div><p>Krylov subspace methods for solving linear systems of equations involving skew-symmetric matrices have gained recent attention. Numerical equivalences among Krylov subspace methods for nonsingular skew-symmetric linear systems have been given in Greif et al. [SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1071–1087]. In this work, we extend the results of Greif et al. to singular skew-symmetric linear systems. In addition, we systematically study three Krylov subspace methods (called S<span>(^3)</span>CG, S<span>(^3)</span>MR, and S<span>(^3)</span>LQ) for solving shifted skew-symmetric linear systems. They all are based on Lanczos triangularization for skew-symmetric matrices and correspond to CG, MINRES, and SYMMLQ for solving symmetric linear systems, respectively. To the best of our knowledge, this is the first work that studies S<span>(^3)</span>LQ. We give some new theoretical results on S<span>(^3)</span>CG, S<span>(^3)</span>MR, and S<span>(^3)</span>LQ. We also provide relations among the three methods and those based on Golub–Kahan bidiagonalization and Saunders–Simon–Yip tridiagonalization. Numerical examples are given to illustrate our theoretical findings.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141725760","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