Linear Algebra and its Applications最新文献_第10页

Weighted parallelogram law, polarization identity, and Clarkson-McCarthy inequalities 加权平行四边形定律，极化同一性和克拉克森-麦卡锡不等式

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-02-01 Epub Date: 2025-10-16 DOI: 10.1016/j.laa.2025.10.015

Fuad Kittaneh , Jorge Losada , Bashar Mayyas

引用次数: 0

Projected tensor-tensor products for efficient computation of optimal multiway data representations 投影张量-张量积用于最优多路数据表示的有效计算

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-09-30 DOI: 10.1016/j.laa.2025.09.018

Katherine Keegan , Elizabeth Newman

{"title":"Projected tensor-tensor products for efficient computation of optimal multiway data representations","authors":"Katherine Keegan , Elizabeth Newman","doi":"10.1016/j.laa.2025.09.018","DOIUrl":"10.1016/j.laa.2025.09.018","url":null,"abstract":"<div><div>Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear factorizations. Behind this matrix-mimetic tensor operation is an invertible matrix whose size depends quadratically on certain dimensions of the data. As a result, for large-scale multiway data, the invertible matrix can be computationally demanding to apply and invert and can lead to inefficient tensor representations in terms of construction and storage costs. In this work, we propose a new projected tensor-tensor product that relaxes the invertibility restriction to reduce computational overhead and still preserves fundamental linear algebraic properties. The transformation behind the projected product is a tall-and-skinny matrix with unitary columns, which depends only linearly on certain dimensions of the data, thereby reducing computational complexity by an order of magnitude. We provide extensive theory to prove the matrix mimeticity and the optimality of compressed representations within the projected product framework. We further prove that projected-product-based approximations outperform a comparable, non-matrix-mimetic tensor factorization. We support the theoretical findings and demonstrate the practical benefits of projected products through numerical experiments on video, hyperspectral imaging, synthetic, and dynamical systems data. All code for this paper is available at <span><span>https://github.com/elizabethnewman/projected-products.git</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 100-147"},"PeriodicalIF":1.1,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204473","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

The Pascal matrix, commuting tridiagonal operators and Fourier algebras 帕斯卡矩阵，交换三对角算子和傅立叶代数

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-10-01 DOI: 10.1016/j.laa.2025.09.023

W. Riley Casper , Ignacio Zurrián

引用次数: 0

RSMAR: An iterative method for range-symmetric linear systems RSMAR：范围对称线性系统的迭代方法

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-09-30 DOI: 10.1016/j.laa.2025.09.024

Kui Du, Jia-Jun Fan, Fang Wang

引用次数: 0

Multiple-term refinements and reverses of real power form for Young-type inequalities via weak submajorization type theorems 基于弱次多数型定理的young型不等式实权形式的多项改进和反演

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-10-10 DOI: 10.1016/j.laa.2025.10.004

Duong Quoc Huy , Thai Thuan Quang , Doan Thi Thuy Van

引用次数: 0

Accurate inverses for SDD1 Z-matrices SDD1 z矩阵的精确逆

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-10-03 DOI: 10.1016/j.laa.2025.09.021

Ping-Fan Dai , Yan-Ping Liu

引用次数: 0

Numerical instability of algebraic rootfinders 代数寻根器的数值不稳定性

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-10-10 DOI: 10.1016/j.laa.2025.10.009

Emil Graf, Alex Townsend

引用次数: 0

The spectral reconstruction problem revisited 光谱重建问题再次被讨论

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-09-29 DOI: 10.1016/j.laa.2025.09.020

Weifang Lv , Wei Wang , Wei Wang , Hao Zhang

{"title":"The spectral reconstruction problem revisited","authors":"Weifang Lv , Wei Wang , Wei Wang , Hao Zhang","doi":"10.1016/j.laa.2025.09.020","DOIUrl":"10.1016/j.laa.2025.09.020","url":null,"abstract":"<div><div>This paper focuses on the following spectral reconstruction problem: Can a graph be uniquely determined (up to isomorphism) by the collection of its spectrum and the spectra of its vertex-deleted graphs? We say two graphs are <em>hyper-cospectral</em> if they share identical spectrum and identical spectra for their vertex-deleted subgraphs. A graph <em>G</em> is <em>spectrally reconstructible</em> (SRC for short) if any graph <em>H</em> that is hyper-cospectral with <em>G</em> is also isomorphic to <em>G</em>. Tutte <span><span>[13]</span></span> showed that graphs with irreducible characteristic polynomials are SRC. We aim to extend this result to a larger family of graphs known as controllable graphs. Since not all controllable graphs are SRC, we address the problem: Which controllable graphs are SRC? We provide a proof for a family of controllable bipartite graphs whose characteristic polynomials have exactly two irreducible factors. Moreover, we demonstrate that for a non-controllable graph <em>G</em> with a characteristic polynomial having exactly two irreducible factors, if a hyper-cospectral graph exists, then their complements are also hyper-cospectral. In addition, we also present an algorithm for determining the spectral reconstructibility of graphs whose characteristic polynomials split into exactly two irreducible factors, as well as for finding their hyper-cospectral mates when they exist. Some examples are also provided to illustrate our results.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 1-23"},"PeriodicalIF":1.1,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204225","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

Maximum spread of graphs without paths of specified length 没有指定长度路径的图的最大扩展

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-09-29 DOI: 10.1016/j.laa.2025.09.019

Wenyan Wang, Yi Wang

{"title":"Maximum spread of graphs without paths of specified length","authors":"Wenyan Wang, Yi Wang","doi":"10.1016/j.laa.2025.09.019","DOIUrl":"10.1016/j.laa.2025.09.019","url":null,"abstract":"<div><div>The spread of a graph is defined as the difference between the largest and smallest eigenvalues of its adjacency matrix. In this paper, we investigate extremal problems for the spread of graphs that forbid paths of a specified length. For <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span> and <em>n</em> sufficiently large, we show that the <em>n</em>-vertex <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub></math></span>-free graph achieving maximum spread is the join of a <em>k</em>-vertex clique and an independent set of <span><math><mi>n</mi><mo>−</mo><mi>k</mi></math></span> vertices. We also show that the extremal graph for <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn><mi>k</mi><mo>+</mo><mn>3</mn></mrow></msub></math></span>-free graphs:<ul><li><span>•</span><span><div>For <span><math><mi>k</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></span>, the spread is maximized by the join of a <em>k</em>-vertex clique with the disjoint union of an edge and an independent set of <span><math><mi>n</mi><mo>−</mo><mi>k</mi><mo>−</mo><mn>2</mn></math></span> vertices.</div></span></li><li><span>•</span><span><div>For <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>, the spread is maximized by the join of a <em>k</em>-vertex clique with an independent set with <span><math><mi>n</mi><mo>−</mo><mi>k</mi></math></span> vertices.</div></span></li></ul></div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"729 ","pages":"Pages 24-48"},"PeriodicalIF":1.1,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204226","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

ρ-Contraction and its consequences ρ——收缩及其后果

IF 1.1 3区数学

Linear Algebra and its Applications Pub Date : 2026-01-15 Epub Date: 2025-10-10 DOI: 10.1016/j.laa.2025.10.007

Hwa-Long Gau , Pei Yuan Wu

引用次数: 0