SIAM Review最新文献_第5页

Landmarks in the History of Iterative Methods 迭代方法历史上的里程碑

IF 10.2 1区数学

SIAM Review Pub Date : 2026-02-09 DOI: 10.1137/24m1680428

Martin J. Gander, Philippe Henry, Gerhard Wanner

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SIGEST 团体

IF 10.2 1区数学

SIAM Review Pub Date : 2026-02-09 DOI: 10.1137/25m1799246

The Editors

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Compositional Function Spaces for Deep Learning 深度学习的组合函数空间

IF 10.2 1区数学

SIAM Review Pub Date : 2026-02-09 DOI: 10.1137/25m1802948

Rahul Parhi, Robert D. Nowak

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Book Review:; Algorithmic Mathematics in Machine Learning 书评:;机器学习中的算法数学

IF 10.2 1区数学

SIAM Review Pub Date : 2025-11-06 DOI: 10.1137/25m1741121

Volker H. Schulz

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Book Review:; Classical Numerical Analysis: A Comprehensive Course 书评:;经典数值分析：一门综合性课程

IF 10.2 1区数学

SIAM Review Pub Date : 2025-11-06 DOI: 10.1137/24m1700983

Guosheng Fu

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Least Squares and the Not-Normal Equations 最小二乘法和非正态方程

IF 10.2 1区数学

SIAM Review Pub Date : 2025-11-06 DOI: 10.1137/23m161851x

Andrew J. Wathen

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On the Loewner Framework, the Kolmogorov Superposition Theorem, and the Curse of Dimensionality 论Loewner框架、Kolmogorov叠加定理和维数诅咒

IF 10.2 1区数学

SIAM Review Pub Date : 2025-11-06 DOI: 10.1137/24m1656657

Athanasios C. Antoulas, Ion Victor Gosea, Charles Poussot-Vassal

{"title":"On the Loewner Framework, the Kolmogorov Superposition Theorem, and the Curse of Dimensionality","authors":"Athanasios C. Antoulas, Ion Victor Gosea, Charles Poussot-Vassal","doi":"10.1137/24m1656657","DOIUrl":"https://doi.org/10.1137/24m1656657","url":null,"abstract":"SIAM Review, Volume 67, Issue 4, Page 737-770, December 2025. <br/> Abstract.The Loewner framework is an interpolatory approach for the approximation of linear and nonlinear systems. The purpose here is to extend this framework to linear parametric systems with an arbitrary number [math] of parameters. To achieve this, a new generalized multivariate rational function realization is proposed. We then introduce the [math]-dimensional multivariate Loewner matrices and show that they can be computed by solving a set of coupled Sylvester equations. The null space of these Loewner matrices allows the construction of multivariate rational functions in barycentric form. The principal result of this work is to show how the null space of [math]-dimensional Loewner matrices can be computed using a sequence of one-dimensional Loewner matrices. Thus, a decoupling of the variables is achieved, which leads to a drastic reduction of the computational burden. Equally importantly, this burden is alleviated by avoiding the explicit construction of large-scale [math]-dimensional Loewner matrices of size [math]. The proposed methodology achieves the decoupling of variables, leading (i) to a reduction in complexity from [math] to below [math] when [math] and (ii) to memory storage bounded by the largest variable dimension rather than their product, thus taming the curse of dimensionality and making the solution scalable to very large data sets. This decoupling of the variables leads to a result similar to the Kolmogorov superposition theorem for rational functions. Thus, making use of barycentric representations, every multivariate rational function can be computed using the composition and superposition of single-variable functions. Finally, we suggest two algorithms (one direct and one iterative) to construct, directly from data, multivariate (or parametric) realizations ensuring (approximate) interpolation. Numerical examples highlight the effectiveness and scalability of the method.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"135 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145448288","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}

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Book Review:; A New Lotka–Volterra Model of Competition With Strategic Aggression: Civil Wars When Strategy Comes into Play 书评:;战略侵略竞争的Lotka-Volterra新模型：战略起作用时的内战

IF 10.2 1区数学

SIAM Review Pub Date : 2025-11-06 DOI: 10.1137/25m1740838

Rikha Rahim, Ahmad F. Sihombing, Ika W. Palupi, Nona T. Sapulette

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Book Review:; Mathematical Analysis: A Very Short Introduction 书评:;数学分析：非常简短的介绍

IF 10.2 1区数学

SIAM Review Pub Date : 2025-11-06 DOI: 10.1137/24m1676211

Anita T. Layton

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Turning Big Data Into Tiny Data: Coresets for Unsupervised Learning Problems 将大数据转化为小数据：无监督学习问题的核心集

IF 10.2 1区数学

SIAM Review Pub Date : 2025-11-06 DOI: 10.1137/25m1799684

Dan Feldman, Melanie Schmidt, Christian Sohler

{"title":"Turning Big Data Into Tiny Data: Coresets for Unsupervised Learning Problems","authors":"Dan Feldman, Melanie Schmidt, Christian Sohler","doi":"10.1137/25m1799684","DOIUrl":"https://doi.org/10.1137/25m1799684","url":null,"abstract":"SIAM Review, Volume 67, Issue 4, Page 801-861, December 2025. <br/> Abstract.We develop and analyze a method to reduce the size of a very large set of data points in a high-dimensional Euclidean space [math] to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set is approximately the same as that for the original point set. For example, computing the first [math] principal components of the reduced set will return approximately the first [math] principal components of the original set, or computing the centers of a [math]-means clustering on the reduced set will return an approximation for the original set. Such a reduced set is also known as a coreset. The main new features of our construction are that the cardinality of the reduced set is independent of the dimension [math] of the input space and that the sets are mergeable [P. K. Agarwal et al., Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI Symposium on Principals of Database Systems, 2012, pp. 23–34]. The latter property means that the union of two reduced sets is a reduced set for the union of the two original sets. It allows us to turn our methods into streaming or distributed algorithms using standard approaches. For problems such as [math]-means and subspace approximation the coreset sizes are also independent of the number of input points. Our method is based on data-dependently projecting the points on a low-dimensional subspace and reducing the cardinality of the points inside this subspace using known methods. The proposed approach works for a wide range of data analysis techniques including [math]-means clustering, principal component analysis, and subspace clustering. The main conceptual contribution is a new coreset definition that allows charging for the costs that appear for every solution to an additive constant.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"53 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145448284","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