SIAM Journal on Matrix Analysis and Applications最新文献_第9页

Block Preconditioners for the Marker-and-Cell Discretization of the Stokes–Darcy Equations Stokes-Darcy方程标记-单元离散化的块预调节器

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-10-18 DOI: 10.1137/22m1518384

Chen Greif, Yunhui He

引用次数: 0

On Characteristic Invariants of Matrix Pencils and Linear Relations 矩阵铅笔的特征不变量与线性关系

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-10-17 DOI: 10.1137/22m1535449

H. Gernandt, F. Martínez Pería, F. Philipp, C. Trunk

引用次数: 1

A Preconditioned MINRES Method for Optimal Control of Wave Equations and its Asymptotic Spectral Distribution Theory 波动方程最优控制的预条件MINRES方法及其渐近谱分布理论

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-10-16 DOI: 10.1137/23m1547251

Sean Hon, Jiamei Dong, Stefano Serra-Capizzano

引用次数: 0

Approximate Solutions of Linear Systems at a Universal Rate 线性系统普遍速率下的近似解

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-09-25 DOI: 10.1137/22m1517196

Stefan Steinerberger

引用次数: 0

Bures–Wasserstein Minimizing Geodesics between Covariance Matrices of Different Ranks 不同秩协方差矩阵间测地线的最小化

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-09-25 DOI: 10.1137/22m149168x

Yann Thanwerdas, Xavier Pennec

{"title":"Bures–Wasserstein Minimizing Geodesics between Covariance Matrices of Different Ranks","authors":"Yann Thanwerdas, Xavier Pennec","doi":"10.1137/22m149168x","DOIUrl":"https://doi.org/10.1137/22m149168x","url":null,"abstract":"The set of covariance matrices equipped with the Bures–Wasserstein distance is the orbit space of the smooth, proper, and isometric action of the orthogonal group on the Euclidean space of square matrices. This construction induces a natural orbit stratification on covariance matrices, which is exactly the stratification by the rank. Thus, the strata are the manifolds of symmetric positive semidefinite matrices of fixed rank endowed with the Bures–Wasserstein Riemannian metric. In this work, we study the geodesics of the Bures–Wasserstein distance. First, we complete the literature on geodesics in each stratum by clarifying the set of preimages of the exponential map and by specifying the injectivity domain. We also give explicit formulae of the horizontal lift, the exponential map, and the Riemannian logarithms that were kept implicit in previous works. Second, we give the expression of all the minimizing geodesic segments joining two covariance matrices of any rank. More precisely, we show that the set of all minimizing geodesics between two covariance matrices and is parametrized by the closed unit ball of for the spectral norm, where are the respective ranks of . In particular, the minimizing geodesic is unique if and only if . Otherwise, there are infinitely many. As a secondary contribution, we provide a review of the definitions related to geodesics in metric spaces, affine connection manifolds, and Riemannian manifolds, which is helpful for the study of other spaces.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135768754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1

An Apocalypse-Free First-Order Low-Rank Optimization Algorithm with at Most One Rank Reduction Attempt per Iteration 每次迭代最多一次降阶尝试的无启示一阶低秩优化算法

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-09-22 DOI: 10.1137/22m1518256

Guillaume Olikier, P.-A. Absil

引用次数: 0

Coseparable Nonnegative Matrix Factorization 可分离非负矩阵分解

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-09-15 DOI: 10.1137/22m1510509

Junjun Pan, Michael K. Ng

{"title":"Coseparable Nonnegative Matrix Factorization","authors":"Junjun Pan, Michael K. Ng","doi":"10.1137/22m1510509","DOIUrl":"https://doi.org/10.1137/22m1510509","url":null,"abstract":"Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under separability assumption, which requires the columns of factor matrix are equal to columns of the input matrix. In this paper, we generalize separability assumption based on 3-factor NMF M=P_1SP_2, and require that S is a sub-matrix of the input matrix. We refer to this NMF as a Co-Separable NMF (CoS-NMF). We discuss some mathematics properties of CoS-NMF, and present the relationships with other related matrix factorizations such as CUR decomposition, generalized separable NMF(GS-NMF), and bi-orthogonal tri-factorization (BiOR-NM3F). An optimization model for CoS-NMF is proposed and alternated fast gradient method is employed to solve the model. Numerical experiments on synthetic datasets, document datasets and facial databases are conducted to verify the effectiveness of our CoS-NMF model. Compared to state-of-the-art methods, CoS-NMF model performs very well in co-clustering task, and preserves a good approximation to the input data matrix as well.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"237 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135353866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1

Randomized Low-Rank Approximation for Symmetric Indefinite Matrices 对称不定矩阵的随机低秩逼近

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-09-08 DOI: 10.1137/22m1538648

Yuji Nakatsukasa, Taejun Park

引用次数: 0

Randomized Block Adaptive Linear System Solvers 随机块自适应线性系统求解器

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-09-06 DOI: 10.1137/22m1488715

Vivak Patel, Mohammad Jahangoshahi, Daniel Adrian Maldonado

引用次数: 0

Sensitivity of Matrix Function Based Network Communicability Measures: Computational Methods and A Priori Bounds 基于矩阵函数的网络通信度量灵敏度:计算方法和先验界

2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-08-31 DOI: 10.1137/23m1556708

Marcel Schweitzer

{"title":"Sensitivity of Matrix Function Based Network Communicability Measures: Computational Methods and A Priori Bounds","authors":"Marcel Schweitzer","doi":"10.1137/23m1556708","DOIUrl":"https://doi.org/10.1137/23m1556708","url":null,"abstract":"When analyzing complex networks, an important task is the identification of those nodes which play a leading role for the overall communicability of the network. In the context of modifying networks (or making them robust against targeted attacks or outages), it is also relevant to know how sensitive the network’s communicability reacts to changes in certain nodes or edges. Recently, the concept of total network sensitivity was introduced in [O. De la Cruz Cabrera, J. Jin, S. Noschese, and L. Reichel, Appl. Numer. Math., 172 (2022) pp. 186–205], which allows one to measure how sensitive the total communicability of a network is to the addition or removal of certain edges. One shortcoming of this concept is that sensitivities are extremely costly to compute when using a straightforward approach (orders of magnitude more expensive than the corresponding communicability measures). In this work, we present computational procedures for estimating network sensitivity with a cost that is essentially linear in the number of nodes for many real-world complex networks. Additionally, we extend the sensitivity concept such that it also covers sensitivity of subgraph centrality and the Estrada index, and we discuss the case of node removal. We propose a priori bounds for these sensitivities which capture well the qualitative behavior and give insight into the general behavior of matrix function based network indices under perturbations. These bounds are based on decay results for Fréchet derivatives of matrix functions with structured, low-rank direction terms which might be of independent interest also for applications other than network analysis.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135890679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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