SIAM J. Sci. Comput.最新文献_第3页

A Ginzburg-Landau-H-1 Model and Its SAV Algorithm for Image Inpainting 图像补漆的Ginzburg-Landau-H-1模型及其SAV算法

SIAM J. Sci. Comput. Pub Date : 2023-06-15 DOI: 10.1007/s10915-023-02252-z

Xiangyun Bai, Jiebao Sun, Jie Shen, Wenjuan Yao, Zhichang Guo

引用次数: 0

Generalized Singleton Bound and List-Decoding Reed-Solomon Codes Beyond the Johnson Radius Johnson半径以外的广义单态定界和列解码Reed-Solomon码

SIAM J. Sci. Comput. Pub Date : 2023-05-23 DOI: 10.1137/20m138795x

Chong Shangguan, Itzhak Tamo

引用次数: 0

Uniform Restricted Chase Termination 制服限制追逐终止

SIAM J. Sci. Comput. Pub Date : 2023-05-23 DOI: 10.1137/20m1377035

Tomasz Gogacz, J. Marcinkowski, Andreas Pieris

引用次数: 0

Higher Order Extended Dynamic Mode Decomposition Based on the Structured Total Least Squares 基于结构化总最小二乘的高阶扩展动态模态分解

SIAM J. Sci. Comput. Pub Date : 2023-04-28 DOI: 10.1137/21m1463665

Weiyang Ding, J. Li

引用次数: 0

Dynamic Finite-Budget Allocation of Stratified Sampling with Adaptive Variance Reduction by Strata 基于分层自适应方差缩减的分层抽样动态有限预算分配

SIAM J. Sci. Comput. Pub Date : 2023-04-28 DOI: 10.1137/21m1430996

Chenxiao Song, Ray Kawai

引用次数: 3

Shape Optimization of the Stokes Eigenvalue Problem Stokes特征值问题的形状优化

SIAM J. Sci. Comput. Pub Date : 2023-04-27 DOI: 10.1137/21m1451543

Jiajie Li, Shengfeng Zhu

引用次数: 0

An Incomplete Cholesky Preconditioner Based on Orthogonal Approximations 基于正交逼近的不完全Cholesky预条件

SIAM J. Sci. Comput. Pub Date : 2023-04-27 DOI: 10.1137/21m1468334

Artem Napov

引用次数: 0

Dynamically Orthogonal Runge-Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation 具有微扰缩回的动态低秩逼近的动态正交龙格-库塔格式

SIAM J. Sci. Comput. Pub Date : 2023-04-27 DOI: 10.1137/21m1431229

A. Charous, Pierre FJ Lermusiaux

{"title":"Dynamically Orthogonal Runge-Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation","authors":"A. Charous, Pierre FJ Lermusiaux","doi":"10.1137/21m1431229","DOIUrl":"https://doi.org/10.1137/21m1431229","url":null,"abstract":". Whether due to the sheer size of a computational domain, the ﬁne resolution required, 5 or the multiples scales and stochasticity of the dynamics, the dimensionality of a system must often 6 be reduced so that problems of interest become computationally tractable. In this paper, we develop 7 retractions for time-integration schemes that eﬃciently and accurately evolve the dynamics of a 8 system’s low-rank approximation. Through diﬀerential geometry, we analyze the error incurred 9 at each time step due to the high-order curvature of the manifold of ﬁxed-rank matrices. We ﬁrst 10 obtain a novel, explicit, computationally inexpensive set of algorithms that we refer to as perturbative 11 retractions and show that the set converges to an ideal retraction that projects optimally and exactly 12 to the manifold of ﬁxed-rank matrices by reducing what we deﬁne as the projection-retraction error. 13 Furthermore, each perturbative retraction itself exhibits high-order convergence to the best low- 14 rank approximation of the full-rank solution. Using perturbative retractions, we then develop a new 15 class of integration techniques that we refer to as dynamically orthogonal Runge-Kutta (DORK) 16 schemes. DORK schemes integrate along the nonlinear manifold, updating the subspace upon which 17 we project the system’s dynamics as it is integrated. Through numerical test cases, we demonstrate 18 our schemes for matrix addition, real-time data compression, and deterministic and stochastic partial 19 diﬀerential equations. We ﬁnd that DORK schemes are highly accurate by incorporating knowledge 20 of the dynamic, nonlinear manifold’s high-order curvature and computationally eﬃcient by limiting 21 the growing rank needed to represent the evolving dynamics. 22 schemes that account for the 774 evolution of the reduced-order integration space during the time-step. We show that 775 DORK schemes are (i) highly accurate by incorporating knowledge of the dynamic, 776 nonlinear manifold’s high-order curvature from stage to stage and (ii) computationally 777 eﬃcient by limiting the growing rank needed to represent the evolving dynamics L . In 778 our real-time data compression example, we show that these retractions may be used 779 when the dynamics are data-driven (rather than model-driven), and the perturbative 780 retractions with high-order corrections drift from the best low-rank approximation at 781 a much slower rate than retractions with low-order corrections. Note that adjusting 782 how the dynamics are calculated to correct the drift in the ﬁrst place is important 783 to obtain the most accurate scheme. Lastly, we show that the retractions may be 784 used in deterministic and stochastic diﬀerential equations: the dynamical low-rank 785 approximation and the retractions are agnostic to the nature of the mathematical 786 spaces we choose to compress, whether deterministic or stochastic. In both cases, the 787 low-rank approximation converges quickly not just to th","PeriodicalId":21812,"journal":{"name":"SIAM J. Sci. Comput.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88368051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

(text{PIN}^{mathcal L}) : Preconditioned Inexact Newton with Learning Capability for Nonlinear System of Equations (text{PIN}^{mathcal L}) 非线性方程组的预条件非精确牛顿学习能力

SIAM J. Sci. Comput. Pub Date : 2023-04-27 DOI: 10.1137/22m1507942

L. Luo, X. Cai

引用次数: 2

Recursive Algorithms to Update a Numerical Basis Matrix of the Null Space of the Block Row, (Banded) Block Toeplitz, and Block Macaulay Matrix 块行、(带状)块Toeplitz和块Macaulay矩阵零空间数值基矩阵更新的递归算法

SIAM J. Sci. Comput. Pub Date : 2023-04-26 DOI: 10.1137/22m1495858

C. Vermeersch, B. Moor

引用次数: 1