SIAM Journal on Matrix Analysis and Applications最新文献

On Substochastic Inverse Eigenvalue Problems with the Corresponding Eigenvector Constraints 论具有相应特征向量约束条件的亚随机反特征值问题

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-09-09 DOI: 10.1137/23m1547305

Yujie Liu, Dacheng Yao, Hanqin Zhang

引用次数: 0

Low-Rank Plus Diagonal Approximations for Riccati-Like Matrix Differential Equations 类似里卡蒂矩阵微分方程的低库加对角近似法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-09-06 DOI: 10.1137/23m1587610

Silvère Bonnabel, Marc Lambert, Francis Bach

{"title":"Low-Rank Plus Diagonal Approximations for Riccati-Like Matrix Differential Equations","authors":"Silvère Bonnabel, Marc Lambert, Francis Bach","doi":"10.1137/23m1587610","DOIUrl":"https://doi.org/10.1137/23m1587610","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1669-1688, September 2024. Abstract. We consider the problem of computing tractable approximations of time-dependent [math] large positive semidefinite (PSD) matrices defined as solutions of a matrix differential equation. We propose to use “low-rank plus diagonal” PSD matrices as approximations that can be stored with a memory cost being linear in the high dimension [math]. To constrain the solution of the differential equation to remain in that subset, we project the derivative at all times onto the tangent space to the subset, following the methodology of dynamical low-rank approximation. We derive a closed-form formula for the projection and show that after some manipulations, it can be computed with a numerical cost being linear in [math], allowing for tractable implementation. Contrary to previous approaches based on pure low-rank approximations, the addition of the diagonal term allows for our approximations to be invertible matrices that can moreover be inverted with linear cost in [math]. We apply the technique to Riccati-like equations, then to two particular problems: first, a low-rank approximation to our recent Wasserstein gradient flow for Gaussian approximation of posterior distributions in approximate Bayesian inference and, second, a novel low-rank approximation of the Kalman filter for high-dimensional systems. Numerical simulations illustrate the results.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"3 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227048","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

Multichannel Frequency Estimation with Constant Amplitude via Convex Structured Low-Rank Approximation 通过凸结构低方根逼近实现恒定振幅的多通道频率估计

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-09-03 DOI: 10.1137/23m1587737

Xunmeng Wu, Zai Yang, Zongben Xu

引用次数: 0

Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics 张量和超图的克朗克积：结构与动力学

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-09-03 DOI: 10.1137/23m1592547

Joshua Pickard, Can Chen, Cooper Stansbury, Amit Surana, Anthony M. Bloch, Indika Rajapakse

{"title":"Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics","authors":"Joshua Pickard, Can Chen, Cooper Stansbury, Amit Surana, Anthony M. Bloch, Indika Rajapakse","doi":"10.1137/23m1592547","DOIUrl":"https://doi.org/10.1137/23m1592547","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1621-1642, September 2024. Abstract. Hypergraphs and tensors extend classic graph and matrix theories to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupling of systems in a graph or matrix context, its utility in studying multiway interactions, such as those represented by tensors and hypergraphs, remains elusive. In this article, we present a comprehensive exploration of algebraic, structural, and spectral properties of the tensor Kronecker product. We express Tucker and tensor train decompositions and various tensor eigenvalues in terms of the tensor Kronecker product. Additionally, we utilize the tensor Kronecker product to form Kronecker hypergraphs, which are tensor-based hypergraph products, and investigate the structure and stability of polynomial dynamics on Kronecker hypergraphs. Finally, we provide numerical examples to demonstrate the utility of the tensor Kronecker product in computing Z-eigenvalues, performing various tensor decompositions, and determining the stability of polynomial systems.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"3 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227050","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

Growth Factors of Orthogonal Matrices and Local Behavior of Gaussian Elimination with Partial and Complete Pivoting 正交矩阵的增长因子以及部分和完全透视高斯消元的局部行为

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-22 DOI: 10.1137/23m1597733

John Peca-Medlin

{"title":"Growth Factors of Orthogonal Matrices and Local Behavior of Gaussian Elimination with Partial and Complete Pivoting","authors":"John Peca-Medlin","doi":"10.1137/23m1597733","DOIUrl":"https://doi.org/10.1137/23m1597733","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1599-1620, September 2024. Abstract. Gaussian elimination (GE) is the most used dense linear solver. Error analysis of GE with selected pivoting strategies on well-conditioned systems can focus on studying the behavior of growth factors. Although exponential growth is possible with GE with partial pivoting (GEPP), growth tends to stay much smaller in practice. Support for this behavior was provided recently by Huang and Tikhomirov’s average-case analysis of GEPP, which showed GEPP growth factors for Gaussian matrices stay at most polynomial with very high probability. GE with complete pivoting (GECP) has also seen a lot of recent interest, with improvements to both lower and upper bounds on worst-case GECP growth provided by Bisain, Edelman, and Urschel in 2023. We are interested in studying how GEPP and GECP behave on the same linear systems as well as studying large growth on particular subclasses of matrices, including orthogonal matrices. Moreover, as a means to better address the question of why large growth is rarely encountered, we further study matrices with a large difference in growth between using GEPP and GECP, and we explore how the smaller growth strategy dominates behavior in a small neighborhood of the initial matrix.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"4 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218079","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 Geometric Approach to Approximating the Limit Set of Eigenvalues for Banded Toeplitz Matrices 近似带状托普利兹矩阵特征值极限集的几何方法

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-22 DOI: 10.1137/23m1587804

Teodor Bucht, Jacob S. Christiansen

{"title":"A Geometric Approach to Approximating the Limit Set of Eigenvalues for Banded Toeplitz Matrices","authors":"Teodor Bucht, Jacob S. Christiansen","doi":"10.1137/23m1587804","DOIUrl":"https://doi.org/10.1137/23m1587804","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1573-1598, September 2024. Abstract. This article is about finding the limit set for banded Toeplitz matrices. Our main result is a new approach to approximate the limit set [math], where [math] is the symbol of the banded Toeplitz matrix. The new approach is geometrical and based on the formula [math], where [math] is a scaling factor, i.e., [math], and [math] denotes the spectrum. We show that the full intersection can be approximated by the intersection for a finite number of [math]’s and that the intersection of polygon approximations for [math] yields an approximating polygon for [math] that converges to [math] in the Hausdorff metric. Further, we show that one can slightly expand the polygon approximations for [math] to ensure that they contain [math]. Then, taking the intersection yields an approximating superset of [math] which converges to [math] in the Hausdorff metric and is guaranteed to contain [math]. Combining the established algebraic (root-finding) method with our approximating superset, we are able to give an explicit bound on the Hausdorff distance to the true limit set. We implement the algorithm in Python and test it. It performs on par to and better in some cases than existing algorithms. We argue, but do not prove, that the average time complexity of the algorithm is [math], where [math] is the number of [math]’s and [math] is the number of vertices for the polygons approximating [math]. Further, we argue that the distance from [math] to both the approximating polygon and the approximating superset decreases as [math] for most of [math], where [math] is the number of elementary operations required by the algorithm.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"22 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218091","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

Random Walks, Conductance, and Resistance for the Connection Graph Laplacian 连接图拉普拉卡的随机漫步、传导和阻力

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-19 DOI: 10.1137/23m1595400

Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn, Sawyer J. Robertson, Zhengchao Wan, Yusu Wang

引用次数: 0

Small Singular Values Can Increase in Lower Precision 小奇异值可提高较低精度

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-12 DOI: 10.1137/23m1557209

Christos Boutsikas, Petros Drineas, Ilse C. F. Ipsen

引用次数: 0

Variational Characterization and Rayleigh Quotient Iteration of 2D Eigenvalue Problem with Applications 二维特征值问题的变分特征和瑞利商迭代及其应用

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-06 DOI: 10.1137/22m1472589

Tianyi Lu, Yangfeng Su, Zhaojun Bai

引用次数: 0

Block-Diagonalization of Quaternion Circulant Matrices with Applications 四元圆周矩阵的对角分块及其应用

IF 1.5 2区数学

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-08-01 DOI: 10.1137/23m1552115

Junjun Pan, Michael K. Ng

{"title":"Block-Diagonalization of Quaternion Circulant Matrices with Applications","authors":"Junjun Pan, Michael K. Ng","doi":"10.1137/23m1552115","DOIUrl":"https://doi.org/10.1137/23m1552115","url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 3, Page 1429-1454, September 2024. Abstract. It is well known that a complex circulant matrix can be diagonalized by a discrete Fourier matrix with imaginary unit [math]. The main aim of this paper is to demonstrate that a quaternion circulant matrix cannot be diagonalized by a discrete quaternion Fourier matrix with three imaginary units [math], [math], and [math]. Instead, a quaternion circulant matrix can be block-diagonalized into 1-by-1 block and 2-by-2 block matrices by permuted discrete quaternion Fourier transform matrix. With such a block-diagonalized form, the inverse of a quaternion circulant matrix can be determined efficiently similarly to the inverse of a complex circulant matrix. We make use of this block-diagonalized form to study quaternion tensor singular value decomposition of quaternion tensors where the entries are quaternion numbers. The applications, including computing the inverse of a quaternion circulant matrix and solving quaternion Toeplitz systems arising from linear prediction of quaternion signals, are employed to validate the efficiency of our proposed block- diagonalized results.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":"49 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141884268","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