SIAM Journal on Matrix Analysis and Applications最新文献_第3页

Erratum: Properties of the Solution Set of Absolute Value Equations and the Related Matrix Classes 勘误：绝对值方程解集及相关矩阵类的性质

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-06-26 DOI: 10.1137/24m1635715

Milan Hladík

引用次数: 0

Fast and Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems 线性系统和特征值问题的快速准确随机算法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-06-20 DOI: 10.1137/23m1565413

Yuji Nakatsukasa, Joel A. Tropp

引用次数: 0

Preconditioner Design via Bregman Divergences 通过布雷格曼发散设计预处理器

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-06-07 DOI: 10.1137/23m1566637

Andreas A. Bock, Martin S. Andersen

引用次数: 0

A Skew-Symmetric Lanczos Bidiagonalization Method for Computing Several Extremal Eigenpairs of a Large Skew-Symmetric Matrix 计算大型偏斜对称矩阵若干极值特征对的偏斜对称兰克佐斯对角线化方法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-06-05 DOI: 10.1137/23m1553029

Jinzhi Huang, Zhongxiao Jia

{"title":"A Skew-Symmetric Lanczos Bidiagonalization Method for Computing Several Extremal Eigenpairs of a Large Skew-Symmetric Matrix","authors":"Jinzhi Huang, Zhongxiao Jia","doi":"10.1137/23m1553029","DOIUrl":"https://doi.org/10.1137/23m1553029","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 2, Page 1114-1147, June 2024. <br/> Abstract. The spectral decomposition of a real skew-symmetric matrix is shown to be equivalent to a specific structured singular value decomposition (SVD) of the matrix. Based on such equivalence, we propose a skew-symmetric Lanczos bidiagonalization (SSLBD) method to compute extremal singular values and the corresponding singular vectors of the matrix, from which its extremal conjugate eigenpairs are recovered pairwise in real arithmetic. A number of convergence results on the method are established, and accuracy estimates for approximate singular triplets are given. In finite precision arithmetic, it is proven that the semi-orthogonality of each set of the computed left and right Lanczos basis vectors and the semi-biorthogonality of two sets of basis vectors are needed to compute the singular values accurately and to make the method work as if it does in exact arithmetic. A commonly used efficient partial reorthogonalization strategy is adapted to maintain the desired semi-orthogonality and semi-biorthogonality. For practical purpose, an implicitly restarted SSLBD algorithm is developed with partial reorthogonalization. Numerical experiments illustrate the effectiveness and overall efficiency of the algorithm.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141257265","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

Differential Geometry with Extreme Eigenvalues in the Positive Semidefinite Cone 正半定锥中具有极值特征值的微分几何

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-06-04 DOI: 10.1137/23m1563906

Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre

{"title":"Differential Geometry with Extreme Eigenvalues in the Positive Semidefinite Cone","authors":"Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre","doi":"10.1137/23m1563906","DOIUrl":"https://doi.org/10.1137/23m1563906","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 2, Page 1089-1113, June 2024. <br/> Abstract. Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields, including computer vision, medical imaging, and machine learning. The dominant geometric paradigm for such applications has consisted of a few Riemannian geometries associated with spectral computations that are costly at high scale and in high dimensions. We present a route to a scalable geometric framework for the analysis and processing of SPD-valued data based on the efficient computation of extreme generalized eigenvalues through the Hilbert and Thompson geometries of the semidefinite cone. We explore a particular geodesic space structure based on Thompson geometry in detail and establish several properties associated with this structure. Furthermore, we define a novel inductive mean of SPD matrices based on this geometry and prove its existence and uniqueness for a given finite collection of points. Finally, we state and prove a number of desirable properties that are satisfied by this mean.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551311","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

Riemannian Preconditioned Coordinate Descent for Low Multilinear Rank Approximation 用于低多线性秩逼近的黎曼预条件坐标后退法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-05-21 DOI: 10.1137/21m1463896

Mohammad Hamed, Reshad Hosseini

引用次数: 0

Probabilistic Rounding Error Analysis of Modified Gram–Schmidt 修正格拉姆-施密特的概率舍入误差分析

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-05-21 DOI: 10.1137/23m1585817

Qinmeng Zou

引用次数: 0

Parameterized Interpolation of Passive Systems 被动系统的参数化内插法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-05-20 DOI: 10.1137/23m1580528

Peter Benner, Pawan Goyal, Paul Van Dooren

引用次数: 0

Spectral Analysis of Preconditioned Matrices Arising from Stage-Parallel Implicit Runge–Kutta Methods of Arbitrarily High Order 任意高阶阶段并行隐式 Runge-Kutta 方法产生的预条件矩阵的频谱分析

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-05-13 DOI: 10.1137/23m1552498

Ivo Dravins, Stefano Serra-Capizzano, Maya Neytcheva

{"title":"Spectral Analysis of Preconditioned Matrices Arising from Stage-Parallel Implicit Runge–Kutta Methods of Arbitrarily High Order","authors":"Ivo Dravins, Stefano Serra-Capizzano, Maya Neytcheva","doi":"10.1137/23m1552498","DOIUrl":"https://doi.org/10.1137/23m1552498","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 2, Page 1007-1034, June 2024. <br/> Abstract. The use of high order fully implicit Runge–Kutta methods is of significant importance in the context of the numerical solution of transient partial differential equations, in particular when solving large scale problems due to fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this study we consider strongly [math]-stable implicit Runge–Kutta methods of arbitrary order of accuracy, based on Radau quadratures, for which efficient preconditioners have been introduced. A refined spectral analysis of the corresponding matrices and matrix sequences is presented, both in terms of localization and asymptotic global distribution of the eigenvalues. Specific expressions of the eigenvectors are also obtained. The given study fully agrees with the numerically observed spectral behavior and substantially improves the theoretical studies done in this direction so far. Concluding remarks and open problems end the current work, with specific attention to the potential generalizations of the hereby suggested general approach.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931836","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 Note on the Randomized Kaczmarz Algorithm for Solving Doubly Noisy Linear Systems 关于解决双噪声线性系统的随机卡兹马兹算法的说明

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-05-06 DOI: 10.1137/23m155712x

El Houcine Bergou, Soumia Boucherouite, Aritra Dutta, Xin Li, Anna Ma

{"title":"A Note on the Randomized Kaczmarz Algorithm for Solving Doubly Noisy Linear Systems","authors":"El Houcine Bergou, Soumia Boucherouite, Aritra Dutta, Xin Li, Anna Ma","doi":"10.1137/23m155712x","DOIUrl":"https://doi.org/10.1137/23m155712x","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 2, Page 992-1006, June 2024. <br/> Abstract. Large-scale linear systems, [math], frequently arise in practice and demand effective iterative solvers. Often, these systems are noisy due to operational errors or faulty data-collection processes. In the past decade, the randomized Kaczmarz algorithm (RK) has been studied extensively as an efficient iterative solver for such systems. However, the convergence study of RK in the noisy regime is limited and considers measurement noise in the right-hand side vector, [math]. Unfortunately, in practice, that is not always the case; the coefficient matrix [math] can also be noisy. In this paper, we analyze the convergence of RK for doubly noisy linear systems, i.e., when the coefficient matrix, [math], has additive or multiplicative noise, and [math] is also noisy. In our analyses, the quantity [math] influences the convergence of RK, where [math] represents a noisy version of [math]. We claim that our analysis is robust and realistically applicable, as we do not require information about the noiseless coefficient matrix, [math], and by considering different conditions on noise, we can control the convergence of RK. We perform numerical experiments to substantiate our theoretical findings.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886693","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