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SIAM Journal on Matrix Analysis and Applications最新文献

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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
{"title":"An Apocalypse-Free First-Order Low-Rank Optimization Algorithm with at Most One Rank Reduction Attempt per Iteration","authors":"Guillaume Olikier, P.-A. Absil","doi":"10.1137/22m1518256","DOIUrl":"https://doi.org/10.1137/22m1518256","url":null,"abstract":"","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136060490","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
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":null,"pages":null},"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
{"title":"Randomized Low-Rank Approximation for Symmetric Indefinite Matrices","authors":"Yuji Nakatsukasa, Taejun Park","doi":"10.1137/22m1538648","DOIUrl":"https://doi.org/10.1137/22m1538648","url":null,"abstract":"","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136299578","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
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
{"title":"Randomized Block Adaptive Linear System Solvers","authors":"Vivak Patel, Mohammad Jahangoshahi, Daniel Adrian Maldonado","doi":"10.1137/22m1488715","DOIUrl":"https://doi.org/10.1137/22m1488715","url":null,"abstract":". Randomized linear solvers leverage randomization to structure-blindly compress and solve a linear system to produce an inexpensive solution. While such a property is highly desirable, randomized linear solvers often suffer when it comes to performance as either (1) problem structure is not being exploited, and (2) hardware is inefficiently used. Thus, randomized adaptive solvers are starting to appear that use the benefits of randomness while attempting to still exploit problem structure and reduce hardware inefficiencies. Unfortunately, such randomized adaptive solvers are likely to be without a theoretical foundation to show that they will work (i.e., find a solution). Accordingly, here, we distill three general criteria for randomized block adaptive solvers, which, as we show, will guarantee convergence of the randomized adaptive solver and supply a worst-case rate of convergence. We will demonstrate that these results apply to existing randomized block adaptive solvers, and to several that we devise for demonstrative purposes.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315847","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
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":null,"pages":null},"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
Analyzing the Influence of Agents in Trust Networks: Applying Nonsmooth Eigensensitivity Theory to a Graph Centrality Problem 信任网络中主体的影响分析:应用非光滑特征敏感性理论求解图中心性问题
IF 1.5 2区 数学
SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-08-30 DOI: 10.1137/21m146884x
Jon Donnelly, Peter G. Stechlinski
{"title":"Analyzing the Influence of Agents in Trust Networks: Applying Nonsmooth Eigensensitivity Theory to a Graph Centrality Problem","authors":"Jon Donnelly, Peter G. Stechlinski","doi":"10.1137/21m146884x","DOIUrl":"https://doi.org/10.1137/21m146884x","url":null,"abstract":"","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64315182","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
A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices 伪对称矩阵的保结构分治方法
2区 数学
SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-08-30 DOI: 10.1137/22m1484985
Peter Benner, Yuji Nakatsukasa, Carolin Penke
{"title":"A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices","authors":"Peter Benner, Yuji Nakatsukasa, Carolin Penke","doi":"10.1137/22m1484985","DOIUrl":"https://doi.org/10.1137/22m1484985","url":null,"abstract":"","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136080656","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
Perturbation Theory of Transfer Function Matrices 传递函数矩阵的微扰理论
2区 数学
SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-08-30 DOI: 10.1137/22m1509825
Vanni Noferini, Lauri Nyman, Javier Pérez, María C. Quintana
{"title":"Perturbation Theory of Transfer Function Matrices","authors":"Vanni Noferini, Lauri Nyman, Javier Pérez, María C. Quintana","doi":"10.1137/22m1509825","DOIUrl":"https://doi.org/10.1137/22m1509825","url":null,"abstract":"Zeros of rational transfer function matrices are the eigenvalues of associated polynomial system matrices under minimality conditions. In this paper, we define a structured condition number for a simple eigenvalue of a (locally) minimal polynomial system matrix , which in turn is a simple zero of its transfer function matrix . Since any rational matrix can be written as the transfer function of a polynomial system matrix, our analysis yields a structured perturbation theory for simple zeros of rational matrices . To capture all the zeros of , regardless of whether they are poles, we consider the notion of root vectors. As corollaries of the main results, we pay particular attention to the special case of being not a pole of since in this case the results get simpler and can be useful in practice. We also compare our structured condition number with Tisseur’s unstructured condition number for eigenvalues of matrix polynomials and show that the latter can be unboundedly larger. Finally, we corroborate our analysis by numerical experiments.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136081554","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
Eigenvalue Embedding of Damped Vibroacoustic System with No-Spillover 无溢出阻尼振动声系统的特征值嵌入
IF 1.5 2区 数学
SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-08-10 DOI: 10.1137/22m1527416
K. Zhao, Zhong Y. Liu
{"title":"Eigenvalue Embedding of Damped Vibroacoustic System with No-Spillover","authors":"K. Zhao, Zhong Y. Liu","doi":"10.1137/22m1527416","DOIUrl":"https://doi.org/10.1137/22m1527416","url":null,"abstract":"","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76183506","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
Revisiting the Matrix Polynomial Greatest Common Divisor 重述矩阵多项式的最大公约数
2区 数学
SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-08-08 DOI: 10.1137/22m1531993
Vanni Noferini, Paul Van Dooren
{"title":"Revisiting the Matrix Polynomial Greatest Common Divisor","authors":"Vanni Noferini, Paul Van Dooren","doi":"10.1137/22m1531993","DOIUrl":"https://doi.org/10.1137/22m1531993","url":null,"abstract":"In this paper, we revisit the greatest common right divisor (GCRD) extraction from a set of polynomial matrices , , with coefficients in a generic field and with common column dimension . We give necessary and sufficient conditions for a matrix to be a GCRD using the Smith normal form of the compound matrix obtained by concatenating vertically, where . We also describe the complete set of degrees of freedom for the solution , and we link it to the Smith form and Hermite form of . We then give an algorithm for constructing a particular minimum size solution for this problem when or , using state-space techniques. This new method works directly on the coefficient matrices of , using orthogonal transformations only. The method is based on the staircase algorithm, applied to a particular pencil derived from a generalized state-space model of .","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135795066","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
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