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Electronic Journal of Linear Algebra最新文献

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A new method to improve the efficiency and accuracy of incremental singular value decomposition 一种提高增量奇异值分解效率和精度的新方法
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-07-07 DOI: 10.13001/ela.2023.7325
Hansi Jiang, A. Chaudhuri
{"title":"A new method to improve the efficiency and accuracy of incremental singular value decomposition","authors":"Hansi Jiang, A. Chaudhuri","doi":"10.13001/ela.2023.7325","DOIUrl":"https://doi.org/10.13001/ela.2023.7325","url":null,"abstract":"Singular value decomposition (SVD) has been widely used in machine learning. It lies at the root of data analysis, and it provides the mathematical basis for many data mining techniques. Recently, interest in incremental SVD has been on the rise because it is well suited to streaming data. In this paper, we propose a new algorithm of incremental SVD that is designed to improve both efficiency and accuracy during computation. More specifically, our proposed algorithm takes advantage of the special structures of arrowhead and diagonal-plus-rank-one matrices involved in updating SVD models to expedite the updating process. Moreover, because the singular values are computed independently, the proposed method can be easily parallelized. In addition, as this paper shows, increasing rank can lead to more accurate singular values in the updating process. Experimental results from synthetic and real data sets demonstrate gains in efficiency and accuracy in the updating process.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46085697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Nullities of cycle-spliced bipartite graphs 环拼接二部图的零性
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-06-10 DOI: 10.13001/ela.2023.7377
Sarula Chang, Jianxi Li, Yirong Zheng
{"title":"Nullities of cycle-spliced bipartite graphs","authors":"Sarula Chang, Jianxi Li, Yirong Zheng","doi":"10.13001/ela.2023.7377","DOIUrl":"https://doi.org/10.13001/ela.2023.7377","url":null,"abstract":"For a simple graph $G$, let $eta(G)$ and $c(G)$ be the nullity and the cyclomatic number of $G$, respectively. A cycle-spliced bipartite graph is a connected graph in which every block is an even cycle. It was shown by Wong et al. (2022) that for every cycle-spliced bipartite graph $G$, $0leqeta(G)leq c(G)+1$. Moreover, the extremal graphs with $eta(G) = c(G)+1$ and $eta(G) =0$, respectively, have been characterized. In this paper, we prove that there is no cycle-spliced bipartite graphs $G$ of any order with nullity $eta(G)=c(G)$. Furthermore, we also provide a structural characterization on cycle-spliced bipartite graphs $G$ with nullity $eta(G)=c(G)-1$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42758020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On the numerical range of Kac-Sylvester matrices 关于Kac-Sylvester矩阵的数值范围
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-05-19 DOI: 10.13001/ela.2023.7703
N. Bebiano, R. Lemos, G. Soares
{"title":"On the numerical range of Kac-Sylvester matrices","authors":"N. Bebiano, R. Lemos, G. Soares","doi":"10.13001/ela.2023.7703","DOIUrl":"https://doi.org/10.13001/ela.2023.7703","url":null,"abstract":"In this paper, the boundary generating curves and the numerical range of Kac-Sylvester matrices up to the order $9$ are characterized. Based on the obtained results and on several computational experiments performed with the Mathematica and MatLab programs, we conjecture that the found types of algebraic curves, namely ellipses and ovals, will appear for an arbitrary order.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43380761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Multi-alternating sign matrices 多重交替符号矩阵
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-05-18 DOI: 10.13001/ela.2023.7471
R. Brualdi, G. Dahl
{"title":"Multi-alternating sign matrices","authors":"R. Brualdi, G. Dahl","doi":"10.13001/ela.2023.7471","DOIUrl":"https://doi.org/10.13001/ela.2023.7471","url":null,"abstract":"We introduce a generalization of alternating sign matrices (ASMs) called multiASMs and develop some of their properties. Classes of multiASMs with specified row and column sum vectors $R$ and $S$ extend the classes of $(0,1)$-matrices with specified $R$ and $S$. The special case when $R=S$ is a constant vector, in particular all 2's, is treated in more detail. We also investigate the polytope spanned by a class of multiASMs. Finally, we discuss the possibility of defining a Bruhat order on a class of multiASMs.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43277702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Graph degeneracy and orthogonal vector representations 图的退化性与正交向量表示
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-05-18 DOI: 10.13001/ela.2023.6907
Lon H. Mitchell
{"title":"Graph degeneracy and orthogonal vector representations","authors":"Lon H. Mitchell","doi":"10.13001/ela.2023.6907","DOIUrl":"https://doi.org/10.13001/ela.2023.6907","url":null,"abstract":"We apply a technique of Sinkovic and van der Holst for constructing orthogonal vector representations of a graph whose complement has given treewidth to graphs whose complement has given degeneracy.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47099055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Refinement of von Neumann-type inequalities on product Eaton triples 乘积伊顿三元组上von neumann型不等式的细化
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-05-17 DOI: 10.13001/ela.2023.7375
M. Niezgoda
{"title":"Refinement of von Neumann-type inequalities on product Eaton triples","authors":"M. Niezgoda","doi":"10.13001/ela.2023.7375","DOIUrl":"https://doi.org/10.13001/ela.2023.7375","url":null,"abstract":"In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where $ V $ is a real inner product space, $ G $ is a compact subgroup of the orthogonal group $ O (V) $, and $ D subset V $ is a closed convex cone. By using an inner structure of an Eaton triple, a refinement of this inequality is shown. In the special case $ G = O ( V ) $, a refinement of the Cauchy-Schwarz inequality is obtained.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43552752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Adapted AZNN methods for time-varying and static matrix problems 时变和静态矩阵问题的自适应AZNN方法
4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-05-04 DOI: 10.13001/ela.2023.7417
Frank Uhlig
{"title":"Adapted AZNN methods for time-varying and static matrix problems","authors":"Frank Uhlig","doi":"10.13001/ela.2023.7417","DOIUrl":"https://doi.org/10.13001/ela.2023.7417","url":null,"abstract":"We present adapted Zhang neural networks (AZNN) in which the parameter settings for the exponential decay constant $eta$ and the length of the start-up phase of basic ZNN are adapted to the problem at hand. Specifically, we study experiments with AZNN for time-varying square matrix factorizations as a product of time-varying symmetric matrices and for the time-varying matrix square roots problem. Differing from generally used small $eta$ values and minimal start-up length phases in ZNN, we adapt the basic ZNN method to work with large or even gigantic $eta$ settings and arbitrary length start-ups using Euler's low accuracy finite difference formula. These adaptations improve the speed of AZNN's convergence and lower its solution error bounds for our chosen problems significantly to near machine constant or even lower levels. Parameter-varying AZNN also allows us to find full rank symmetrizers of static matrices reliably, for example, for the Kahan and Frank matrices and for matrices with highly ill-conditioned eigenvalues and complicated Jordan structures of dimensions from $n = 2$ on up. This helps in cases where full rank static matrix symmetrizers have never been successfully computed before.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136375307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Relation between the row left rank of a quaternion unit gain graph and the rank of its underlying graph 四元数单位增益图的左行秩与其底层图的秩之间的关系
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-04-20 DOI: 10.13001/ela.2023.7681
Qiannan Zhou, Yong Lu
{"title":"Relation between the row left rank of a quaternion unit gain graph and the rank of its underlying graph","authors":"Qiannan Zhou, Yong Lu","doi":"10.13001/ela.2023.7681","DOIUrl":"https://doi.org/10.13001/ela.2023.7681","url":null,"abstract":"Let $Phi=(G,U(mathbb{Q}),varphi)$ be a quaternion unit gain graph (or $U(mathbb{Q})$-gain graph), where $G$ is the underlying graph of $Phi$, $U(mathbb{Q})={zin mathbb{Q}: |z|=1}$ is the circle group, and $varphi:overrightarrow{E}rightarrow U(mathbb{Q})$ is the gain function such that $varphi(e_{ij})=varphi(e_{ji})^{-1}=overline{varphi(e_{ji})}$. Let $A(Phi)$ be the adjacency matrix of $Phi$ and $r(Phi)$ be the row left rank of $Phi$. In this paper, we prove that $-2c(G)leq r(Phi)-r(G)leq 2c(G)$, where $r(G)$ and $c(G)$ are the rank and the dimension of cycle space of $G$, respectively. All corresponding extremal graphs are characterized. The results will generalize the corresponding results of signed graphs (Lu et al. [20] and Wang [33]), mixed graphs (Chen et al. [7]), and complex unit gain graphs (Lu et al. [21]).","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45864098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Centered PSD matrices with thin spectrum are M-matrices 具有薄谱的中心PSD矩阵是M-矩阵
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-04-17 DOI: 10.13001/ela.2023.7051
K. Devriendt
{"title":"Centered PSD matrices with thin spectrum are M-matrices","authors":"K. Devriendt","doi":"10.13001/ela.2023.7051","DOIUrl":"https://doi.org/10.13001/ela.2023.7051","url":null,"abstract":"We show that real, symmetric, centered (zero row sum) positive semidefinite matrices of order $n$ and rank $n-1$ with eigenvalue ratio $lambda_{max}/lambda_{min}leq n/(n-2)$ between the largest and smallest nonzero eigenvalue have nonpositive off-diagonal entries, and that this eigenvalue criterion is tight. The result is relevant in the context of matrix theory and inverse eigenvalue problems, and we discuss an application to Laplacian matrices.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45409479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Products of skew-involutions 斜对合的乘积
IF 0.7 4区 数学
Electronic Journal of Linear Algebra Pub Date : 2023-04-07 DOI: 10.13001/ela.2023.7709
Jesus Paolo Joven, Agnes T. Paras
{"title":"Products of skew-involutions","authors":"Jesus Paolo Joven, Agnes T. Paras","doi":"10.13001/ela.2023.7709","DOIUrl":"https://doi.org/10.13001/ela.2023.7709","url":null,"abstract":"It is shown that every $2n$-by-$2n$ matrix over a field $mathbb{F}$ with determinant 1 is a product of (i) four or fewer skew-involutions ($A^2 = -I$) provided $mathbb{F} neq mathbb{Z}_3$, and (ii) eight or fewer skew-involutions if $mathbb{F} = mathbb{Z}_3$ and $n > 1$. Every real symplectic matrix is a product of six real symplectic skew-involutions, and an explicit factorization of a complex symplectic matrix into two symplectic skew-involutions is given.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48612640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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