arXiv - CS - Numerical Analysis最新文献_第8页

The Existence the Solution of Nonlinear Discrete Schemes and Convergence of a Linearized Iterative Method for time-dependent PNP Equations 时变PNP方程的非线性离散格式的存在性、解和线性化迭代法的收敛性

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00291

Yang Liu, Shi Shu, Ying Yang

引用次数: 0

Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds 多项式映射流形模型约简的近似界

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00724

Patrick Buchfink, Silke Glas, Bernard Haasdonk

引用次数: 0

Minimal rank factorizations of polynomial matrices 多项式矩阵的最小秩分解

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00676

Andrii Dmytryshyn, Froilán Dopico, Paul Van Dooren

{"title":"Minimal rank factorizations of polynomial matrices","authors":"Andrii Dmytryshyn, Froilán Dopico, Paul Van Dooren","doi":"arxiv-2312.00676","DOIUrl":"https://doi.org/arxiv-2312.00676","url":null,"abstract":"We investigate rank revealing factorizations of rank deficient $m times n$\u0000polynomial matrices $P(lambda)$ into products of three, $P(lambda) =\u0000L(lambda) E(lambda) R(lambda)$, or two, $P(lambda) = L(lambda)\u0000R(lambda)$, polynomial matrices. Among all possible factorizations of these\u0000types, we focus on those for which $L(lambda)$ and/or $R(lambda)$ is a\u0000minimal basis, since they allow us to relate easily the degree of $P(lambda)$\u0000with some degree properties of the factors. We call these factorizations\u0000minimal rank factorizations. Motivated by the well-known fact that,\u0000generically, rank deficient polynomial matrices over the complex field do not\u0000have eigenvalues, we pay particular attention to the properties of the minimal\u0000rank factorizations of polynomial matrices without eigenvalues. We carefully\u0000analyze the degree properties of generic minimal rank factorizations in the set\u0000of complex $m times n$ polynomial matrices with normal rank at most $r$ and\u0000degree at most $d$, and we prove that they are of the form $L(lambda)\u0000R(lambda)$, where the degrees of the $r$ columns of $L(lambda)$ differ at\u0000most by one, the degrees of the $r$ rows of $R(lambda)$ differ at most by one,\u0000and, for each $i=1, ldots, r$, the sum of the degrees of the $i$th column of\u0000$L(lambda)$ and of the $i$th row of $R(lambda)$ is equal to $d$. Finally, we\u0000show how these sets of polynomial matrices with generic factorizations are\u0000related to the sets of polynomial matrices with generic eigenstructures.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 27","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494187","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: 0

Nonlinear-manifold reduced order models with domain decomposition 具有域分解的非线性流形降阶模型

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00713

Alejandro N. Diaz, Youngsoo Choi, Matthias Heinkenschloss

{"title":"Nonlinear-manifold reduced order models with domain decomposition","authors":"Alejandro N. Diaz, Youngsoo Choi, Matthias Heinkenschloss","doi":"arxiv-2312.00713","DOIUrl":"https://doi.org/arxiv-2312.00713","url":null,"abstract":"A nonlinear-manifold reduced order model (NM-ROM) is a great way of\u0000incorporating underlying physics principles into a neural network-based\u0000data-driven approach. We combine NM-ROMs with domain decomposition (DD) for\u0000efficient computation. NM-ROMs offer benefits over linear-subspace ROMs\u0000(LS-ROMs) but can be costly to train due to parameter scaling with the\u0000full-order model (FOM) size. To address this, we employ DD on the FOM, compute\u0000subdomain NM-ROMs, and then merge them into a global NM-ROM. This approach has\u0000multiple advantages: parallel training of subdomain NM-ROMs, fewer parameters\u0000than global NM-ROMs, and adaptability to subdomain-specific FOM features. Each\u0000subdomain NM-ROM uses a shallow, sparse autoencoder, enabling hyper-reduction\u0000(HR) for improved computational speed. In this paper, we detail an algebraic DD\u0000formulation for the FOM, train HR-equipped NM-ROMs for subdomains, and\u0000numerically compare them to DD LS-ROMs with HR. Results show a significant\u0000accuracy boost, on the order of magnitude, for the proposed DD NM-ROMs over DD\u0000LS-ROMs in solving the 2D steady-state Burgers' equation.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"39 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503958","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: 0

A Preconditioned Interior Point Method for Support Vector Machines Using an ANOVA-Decomposition and NFFT-Based Matrix-Vector Products 基于anova分解和nfft矩阵向量积的支持向量机预条件内点法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00538

Theresa Wagner, John W. Pearson, Martin Stoll

引用次数: 0

On Novel Fixed-Point-Type Iterations with Structure-Preserving Doubling Algorithms for Stochastic Continuous-time Algebraic Riccati equations 随机连续时间代数Riccati方程的新颖不动点型迭代保结构加倍算法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00328

Tsung-Ming Huang, Yueh-Cheng Kuo, Ren-Cang Li, Wen-Wei Lin

{"title":"On Novel Fixed-Point-Type Iterations with Structure-Preserving Doubling Algorithms for Stochastic Continuous-time Algebraic Riccati equations","authors":"Tsung-Ming Huang, Yueh-Cheng Kuo, Ren-Cang Li, Wen-Wei Lin","doi":"arxiv-2312.00328","DOIUrl":"https://doi.org/arxiv-2312.00328","url":null,"abstract":"In this paper we mainly propose efficient and reliable numerical algorithms\u0000for solving stochastic continuous-time algebraic Riccati equations (SCARE)\u0000typically arising from the differential statedependent Riccati equation\u0000technique from the 3D missile/target engagement, the F16 aircraft flight\u0000control and the quadrotor optimal control etc. To this end, we develop a fixed\u0000point (FP)-type iteration with solving a CARE by the structure-preserving\u0000doubling algorithm (SDA) at each iterative step, called FP-CARE SDA. We prove\u0000that either the FP-CARE SDA is monotonically nondecreasing or nonincreasing,\u0000and is R-linearly convergent, with the zero initial matrix or a special initial\u0000matrix satisfying some assumptions. The FP-CARE SDA (FPC) algorithm can be\u0000regarded as a robust initial step to produce a good initial matrix, and then\u0000the modified Newton (mNT) method can be used by solving the corresponding\u0000Lyapunov equation with SDA (FPC-mNT-Lyap SDA). Numerical experiments show that\u0000the FPC-mNT-Lyap SDA algorithm outperforms the other existing algorithms.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"231 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138517389","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: 0

WENO based adaptive image zooming algorithm 基于WENO的自适应图像缩放算法

arXiv - CS - Numerical Analysis Pub Date : 2023-11-30 DOI: arxiv-2312.00229

Bojan Crnković, Jerko Škifić, Tina Bosner

引用次数: 0

Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball 用切比雪夫多项式网格计算立方体、单纯形和球上的勒贝格常数

arXiv - CS - Numerical Analysis Pub Date : 2023-11-30 DOI: arxiv-2311.18656

L. Bialas-Ciez, D. J. Kenne, A. Sommariva, M. Vianello

引用次数: 0

Accelerating Flow Simulations using Online Dynamic Mode Decomposition 利用在线动态模态分解加速流动模拟

arXiv - CS - Numerical Analysis Pub Date : 2023-11-30 DOI: arxiv-2311.18715

Seung Won Suh, Seung Whan Chung, Peer-Timo Bremer, Youngsoo Choi