Linear Algebra and its Applications最新文献_第5页

Spectral radius, the matching number and fractional criticality of graphs 谱半径，匹配数和分数临界图

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-03-01 Epub Date: 2025-11-26 DOI: 10.1016/j.laa.2025.11.020

Huicai Jia , Ao Fan , Ruifang Liu

{"title":"Spectral radius, the matching number and fractional criticality of graphs","authors":"Huicai Jia , Ao Fan , Ruifang Liu","doi":"10.1016/j.laa.2025.11.020","DOIUrl":"10.1016/j.laa.2025.11.020","url":null,"abstract":"<div><div>The binding number <math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo></math> of a graph G is the minimum value of <math><mo>|</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>|</mo><mo>/</mo><mo>|</mo><mi>X</mi><mo>|</mo></math> taken over all non-empty subsets X of <math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math> such that <math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>≠</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math>. A graph G is called 1-binding if <math><mi>b</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mn>1</mn></math>. The matching number of G, denoted by <math><mi>ν</mi><mo>(</mo><mi>G</mi><mo>)</mo></math>, is the size of a maximum matching in G. In this paper, we focus on characterizing structural properties from the spectral perspective. Inspired by the elegant result of Fan and Lin (2024) [16] on the existence of a perfect matching in 1-binding graphs, we adopt the double eigenvector technique due to Rowlinson and present a tight sufficient condition in terms of the spectral radius for a connected 1-binding graph to guarantee <math><mi>ν</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>></mo><mfrac><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math>.</div><div>Let <math><mi>r</mi><mo>≥</mo><mn>1</mn></math> be a given integer. A graph G is fractional ID-<math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math>-factor-critical if for every independent set I of G with <math><mo>|</mo><mi>I</mi><mo>|</mo><mo>=</mo><mi>r</mi></math>, <math><mi>G</mi><mo>−</mo><mi>I</mi></math> has a fractional <math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math>-factor. We first propose a sufficient condition based on the number of edges for a graph to be fractional ID-<math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math>-factor-critical. As an application, we take full advantage of the spectral bound and obtain a sufficient condition in terms of the spectral radius for a graph to be fractional ID-<math><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math>-factor-critical, which extends nicely the result of Fan et al. (2024) [12] from <math><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>1</mn></math> to general a and b.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"732 ","pages":"Pages 1-17"},"PeriodicalIF":1.1,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145617422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Covariant decomposable maps on C*-algebras and quantum dynamics C*-代数上的协变可分解映射与量子动力学

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-04 DOI: 10.1016/j.laa.2025.12.002

Krzysztof Szczygielski

引用次数: 0

On the loss of orthogonality in low-synchronization variants of reorthogonalized block classical Gram-Schmidt 重正交化块的低同步变体的正交性损失

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-02 DOI: 10.1016/j.laa.2025.11.018

Erin Carson , Kathryn Lund , Yuxin Ma , Eda Oktay

{"title":"On the loss of orthogonality in low-synchronization variants of reorthogonalized block classical Gram-Schmidt","authors":"Erin Carson , Kathryn Lund , Yuxin Ma , Eda Oktay","doi":"10.1016/j.laa.2025.11.018","DOIUrl":"10.1016/j.laa.2025.11.018","url":null,"abstract":"<div><div>Interest in communication-avoiding orthogonalization schemes for high-performance computing has been growing recently. This manuscript addresses open questions about the numerical stability of various block classical Gram-Schmidt variants that have been proposed in the past few years. An abstract framework is employed, the flexibility of which allows for new rigorous bounds on the loss of orthogonality in these variants. We first analyze a generalization of (reorthogonalized) block classical Gram-Schmidt and show that a “strong” intrablock orthogonalization routine is only needed for the very first block in order to maintain orthogonality on the level of the unit roundoff. In particular, this “strong” first step does not have to be a reorthogonalized QR itself and subsequent steps can use less stable QR variants, thus keeping the overall communication costs low.</div><div>Then, using this variant, which has four synchronization points per block column, we remove the synchronization points one at a time and analyze how each alteration affects the stability of the resulting method. Our analysis shows that the variant requiring only one synchronization per block column, equivalent to a variant previously proposed in the literature, cannot be guaranteed to be stable in practice, as stability begins to degrade with the first reduction of synchronization points. As a negative result, we conclude that this particular block algorithm should be avoided in practice.</div><div>Our analysis of block methods also provides new, more positive theoretical results for the single-column case. In particular, it is proven that DCGS2 from (Bielich et al., 2022 [5]) and CGS-2 from (Świrydowicz et al., 2021 [10]) are as stable as Householder QR. Numerical examples from the BlockStab toolbox are included throughout, to help compare variants and illustrate the effects of different choices of intraorthogonalization subroutines.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"732 ","pages":"Pages 162-206"},"PeriodicalIF":1.1,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145733920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Dilating contractions into involutions and projections 将宫缩扩张为内联和凸出

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-01 DOI: 10.1016/j.laa.2025.11.022

Jean-Christophe Bourin , Eun-Young Lee

引用次数: 0

Comparing the operator norms of symmetric matrices sharing the same numerical range 比较具有相同数值范围的对称矩阵的算子范数

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-05 DOI: 10.1016/j.laa.2025.12.004

Mao-Ting Chien , Hiroshi Nakazato

引用次数: 0

Every expansive m-concave operator has m-isometric dilation 每一个膨胀m-凹算子都有m-等距膨胀

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-03-01 Epub Date: 2025-12-03 DOI: 10.1016/j.laa.2025.12.001

Michał Buchała

引用次数: 0

Gradings and graded identities of null-filiform Leibniz algebras 零丝形莱布尼兹代数的分级和分级恒等式

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-02-15 Epub Date: 2025-11-10 DOI: 10.1016/j.laa.2025.11.003

Lucio Centrone , Luís Fertunani , Claudemir Fideles

引用次数: 0

Generalizing Lee's conjecture on the sum of absolute values of matrices 推广李氏关于矩阵绝对值和的猜想

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-02-15 Epub Date: 2025-11-19 DOI: 10.1016/j.laa.2025.11.015

Quanyu Tang, Shu Zhang

引用次数: 0

Some applications of the (p,r,s) halves of the Riordan arrays Riordan数组（p,r,s）半部分的一些应用

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-02-15 Epub Date: 2025-11-11 DOI: 10.1016/j.laa.2025.11.008

Yasemin Alp

引用次数: 0

The P-vertex problem for symmetric matrices whose associated graphs admit perfect matchings 关联图完全匹配的对称矩阵的p顶点问题

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-02-15 Epub Date: 2025-11-11 DOI: 10.1016/j.laa.2025.11.009

K. Sharma, S.K. Panda

{"title":"The P-vertex problem for symmetric matrices whose associated graphs admit perfect matchings","authors":"K. Sharma, S.K. Panda","doi":"10.1016/j.laa.2025.11.009","DOIUrl":"10.1016/j.laa.2025.11.009","url":null,"abstract":"<div><div>Let G be the underlying graph of a real symmetric matrix A. Denote by <math><mi>A</mi><mo>(</mo><mi>j</mi><mo>)</mo></math> the principal submatrix of A obtained by deleting the jth row and column, and let <math><msub><mrow><mi>m</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></math> denote the algebraic multiplicity of the eigenvalue <math><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub></math> of A. An index j is called a P-vertex of A if <math><msub><mrow><mi>m</mi></mrow><mrow><mi>A</mi><mo>(</mo><mi>j</mi><mo>)</mo></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>−</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>1</mn></math>. A graph G on n vertices is said to have property (P) if there exists a nonsingular symmetric matrix A whose underlying graph is G such that every vertex of A is a P-vertex. This work develops a graph-theoretic framework for studying property (P), with particular emphasis on graphs that admit a perfect matching. We analyze bipartite graphs that satisfy property (P) and show that the existence of a perfect matching plays a decisive role in their characterization. In particular, we prove that a tree possesses property (P) if and only if it admits a unique perfect matching, and we present an alternative characterization of unicyclic graphs satisfying property (P). The analysis is then extended to non-bipartite graphs with a unique perfect matching, where we highlight structural features that influence property (P). Furthermore, we construct a family of graphs on n vertices that do not satisfy property (P), but have a nonsingular matrix for which the number of P-vertices is <math><mi>n</mi><mo>−</mo><mn>1</mn></math>. We also investigate the behavior of property (P) under certain graph operations, such as the edge-joining of graphs, and show that this operation preserves property (P) under specific conditions. In particular, we establish that if two graphs G and H each satisfy property (P), then the graph obtained by joining them with a single edge also satisfies property (P), and we examine the converse of this result.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"731 ","pages":"Pages 109-138"},"PeriodicalIF":1.1,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145577893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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