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Book Review:; Fast Matrix Multiplication with Applications 书评:;快速矩阵乘法及其应用
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-08-06 DOI: 10.1137/25m1773933
Markus Bläser
{"title":"Book Review:; Fast Matrix Multiplication with Applications","authors":"Markus Bläser","doi":"10.1137/25m1773933","DOIUrl":"https://doi.org/10.1137/25m1773933","url":null,"abstract":"SIAM Review, Volume 68, Issue 3, Page 689-690, September 2026. <br/> Abstract.This book provides an in-depth treatment, including full proofs, of the development of fast matrix multiplication algorithms following the discovery of Strassen’s algorithm or, more precisely, Winograd’s algorithm a year earlier, although the latter cannot be applied recursively. The development is described up to Schönhage’s tau theorem. The author places special emphasis on exact algorithms for multiplying matrices of small formats, which are particularly well suited for designing practically relevant algorithms through recursive application. In addition, the book concludes with a range of applications, such as computing other linear algebra problems in matrix multiplication time.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"84 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148688001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Book Review:; Spline Functions: More Computational Methods 书评:;样条函数：更多的计算方法
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-08-06 DOI: 10.1137/25m1809161
Michael Floater
{"title":"Book Review:; Spline Functions: More Computational Methods","authors":"Michael Floater","doi":"10.1137/25m1809161","DOIUrl":"https://doi.org/10.1137/25m1809161","url":null,"abstract":"SIAM Review, Volume 68, Issue 3, Page 691-692, September 2026. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"9 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148687776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Research Spotlights 研究聚光灯
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-08-06 DOI: 10.1137/26m1903222
Stefan M. Wild
{"title":"Research Spotlights","authors":"Stefan M. Wild","doi":"10.1137/26m1903222","DOIUrl":"https://doi.org/10.1137/26m1903222","url":null,"abstract":"SIAM Review, Volume 68, Issue 3, Page 577-577, September 2026. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"460 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148687821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
SIGEST 团体
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-08-06 DOI: 10.1137/26m1903258
The Editors
{"title":"SIGEST","authors":"The Editors","doi":"10.1137/26m1903258","DOIUrl":"https://doi.org/10.1137/26m1903258","url":null,"abstract":"SIAM Review, Volume 68, Issue 3, Page 609-610, September 2026. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"1 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148687819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Education 教育
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-05-13 DOI: 10.1137/26m1862212
Hélène Frankowska
{"title":"Education","authors":"Hélène Frankowska","doi":"10.1137/26m1862212","DOIUrl":"https://doi.org/10.1137/26m1862212","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 405-405, June 2026. <br/>","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"30 1","pages":"405-405"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Bounds on Small Ramsey Numbers by Semidefinite Programming 半定规划下小Ramsey数的界
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-05-13 DOI: 10.1137/25m1827554
Bernard Lidický, Florian Pfender
{"title":"Bounds on Small Ramsey Numbers by Semidefinite Programming","authors":"Bernard Lidický, Florian Pfender","doi":"10.1137/25m1827554","DOIUrl":"https://doi.org/10.1137/25m1827554","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 385-403, June 2026. <br/> Abstract.Finding exact Ramsey numbers is a problem typically restricted to relatively small graphs. The flag algebra method introduced by Razborov in 2007 was developed to find asymptotic results for very large graphs, so it seems that the method should not be suitable for finding small Ramsey numbers. But this intuition is wrong, and we will develop a technique to do just that in this paper. We find new upper bounds for many small graph and hypergraph Ramsey numbers. As a result, we prove several exact values. The main power of the method relies on utilizing semidefinite programming to find certificates that are sums of squares. We hope that this technique will be adapted to address other questions for smaller graphs with the flag algebra method.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"33 1","pages":"385-403"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Book Review:; Non-Local Cell Adhesion Models: Symmetries and Bifurcations in 1-D 书评:;非局部细胞粘附模型：1-D的对称性和分岔
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-05-13 DOI: 10.1137/24m1721384
Nadia Loy
{"title":"Book Review:; Non-Local Cell Adhesion Models: Symmetries and Bifurcations in 1-D","authors":"Nadia Loy","doi":"10.1137/24m1721384","DOIUrl":"https://doi.org/10.1137/24m1721384","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 463-464, June 2026. <br/> If you’ve ever wondered how math and biology can play complex, yet harmonious jazz, this book is your backstage pass. Non-Local Cell Adhesion Models: Symmetries and Bifurcations in 1-D takes you on an intellectually thrilling journey starting from a rather (apparently) humble but powerfully insightful heuristic model introduced by Armstrong, Painter, and Sherratt. Despite its seemingly simple beginnings, this model, a nonlocal nonlinear PDE, is a heavyweight champion in applied mathematics capable of mimicking certain cell sorting experiments in the fascinating and fundamental realm of cell adhesion.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"30 1","pages":"463-464"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Tauberian Identities and Suspended Falls: A Wile E. Coyote Time Lag in the Fall of Stretched Elastic Bodies 陶伯利恒等式与悬落：拉伸弹性体下落中的一个时间差
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-05-13 DOI: 10.1137/23m157377x
Roberto Camassa, Richard M. McLaughlin
{"title":"Tauberian Identities and Suspended Falls: A Wile E. Coyote Time Lag in the Fall of Stretched Elastic Bodies","authors":"Roberto Camassa, Richard M. McLaughlin","doi":"10.1137/23m157377x","DOIUrl":"https://doi.org/10.1137/23m157377x","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 407-422, June 2026. <br/> Abstract.The application of the motion of a vertically suspended mass-spring system released under tension is studied, focusing upon the delay timescale for the bottom mass fall as a function of the spring constants and masses. This “hang-time,” reminiscent of the Coyote and Road Runner cartoons, is quantified using the far field asymptotic expansion of the bottom mass’s Laplace transform. These asymptotics are connected to the short time mass dynamics through Tauberian identities and explicit residue calculations. It is shown, perhaps paradoxically, that this delay timescale is maximized in the large mass limit of the top “boulder.” Experiments are presented and compared with the theoretical predictions. This system is an exciting example for the teaching of mass-spring dynamics in classes on ordinary differential equations and does not require any normal mode calculations for these predictions.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"434 1","pages":"407-422"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Localized Patterns 本地化模式
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-05-13 DOI: 10.1137/24m165658x
Jason J. Bramburger, Dan J. Hill, David J. B. Lloyd
{"title":"Localized Patterns","authors":"Jason J. Bramburger, Dan J. Hill, David J. B. Lloyd","doi":"10.1137/24m165658x","DOIUrl":"https://doi.org/10.1137/24m165658x","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 217-292, June 2026. <br/> Abstract.Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain-covering patterns (for example, stripes and hexagons) emerge from a pattern-forming/Turing instability, analyzing the emergence of their localized counterparts remains a significant challenge. There has been considerable progress in studying localized patterns over the past few decades, often by employing innovative mathematical tools and techniques. In particular, the study of localized pattern formation has benefited greatly from numerical techniques; the continuing advancement in computational power has helped to both identify new types of pattern and further our understanding of their behavior. We review recent advances regarding the complex behavior of localized patterns and the mathematical tools that have been developed to understand them, covering various topics from spatial dynamics, exponential asymptotics, and numerical methods. We observe that the mathematical understanding of localized patterns decreases as the spatial dimension increases, thus providing significant open problems that will form the basis for future investigations.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"30 1","pages":"217-292"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Featured Review:; Probability Theory: The Logic of Science 评论:;概率论：科学的逻辑
IF 10.2 1区 数学
SIAM Review Pub Date : 2026-05-13 DOI: 10.1137/25m1813883
Krešimir Josić, Michael Buice
{"title":"Featured Review:; Probability Theory: The Logic of Science","authors":"Krešimir Josić, Michael Buice","doi":"10.1137/25m1813883","DOIUrl":"https://doi.org/10.1137/25m1813883","url":null,"abstract":"SIAM Review, Volume 68, Issue 2, Page 459-462, June 2026. <br/> Probability Theory: The Logic of Science by E. T. Jaynes is a highly ambitious, unusual, and personal book. Its goal is no less than to lay the foundation for how to reason under uncertainty, not only in science, but generally. Inspired by Polya’s Mathematics and Plausible Reasoning, throughout his career Jaynes pursued a program of understanding the rules of plausible reasoning that would be broadly applicable across domains. Starting not from axioms, but from the “desiderata,” or desirable properties, that one would like to have in a quantitative system of reasoning, Jaynes arrives at the traditional rules of probability theory, namely, the sum and product rules. In so doing, he argues that probability theory is not constrained to any discipline, but constitutes a widely applicable extension of traditional logical systems, wherein statements have truth values that have a quantifiable uncertainty. Jaynes viewed probability theory as a kind of “theory of everything” for reasoning. The book contains an extensive and impressive collection of examples and discussions aimed at underlining this idea and showing the ways in which it aligns or not with traditional views.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"10 1","pages":"459-462"},"PeriodicalIF":10.2,"publicationDate":"2026-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148288196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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