SIAM Review最新文献_第8页

Education 教育

IF 10.2 1区数学

SIAM Review Pub Date : 2023-02-01 DOI: 10.1137/23n975648

H. Frankowska

引用次数: 0

Survey and Review 调查及检讨

IF 10.2 1区数学

SIAM Review Pub Date : 2023-02-01 DOI: 10.1137/23n975612

M. Hochbruck

引用次数: 0

SIGEST SIGEST

1区数学

SIAM Review Pub Date : 2023-02-01 DOI: 10.1137/23n975636

None The Editors

{"title":"SIGEST","authors":"None The Editors","doi":"10.1137/23n975636","DOIUrl":"https://doi.org/10.1137/23n975636","url":null,"abstract":"The SIGEST article in this issue, “Improbability of Collisions of Point-Vortices in Bounded Planar Domains,” by Martin Donati, is based on the 2022 SIAM Journal on Mathematics Analysis article “Two-Dimensional Point Vortex Dynamics in Bounded Domains: Global Existence for Almost Every Initial Data.” This work concerns point-vortex dynamics in a very general bounded domain in the plane. The main result is that the set of initial configurations which lead to finite-time collision, although nonempty, has Lebesgue measure zero. This is an elegant and highly nontrivial extension to general bounded domains with $C^{2, alpha}$ boundary of a result previously known only for three domains: the full plane, a disk, and the complement of a disk. It is notable that the result also extends to point-vortex dynamics in multiply connected domains. In preparing this SIGEST version, the author has added a new introductory section that explains the context of the new results. Moreover, some of the technical details from the original article have been replaced by more accessible high-level explanations. Recent references on the topics of vortex collisions and desingularization problems are also included. This SIGEST article will be of particular interest to researchers in fluid mechanics, partial differential equations, and applied analysis.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136252628","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

Improbability of Collisions of Point-Vortices in Bounded Planar Domains 有界平面区域中点涡碰撞的非概率性

IF 10.2 1区数学

SIAM Review Pub Date : 2023-02-01 DOI: 10.1137/22m1523340

M. Donati

引用次数: 0

SIGEST

IF 10.2 1区数学

SIAM Review Pub Date : 2022-11-03 DOI: 10.1137/22n975573

The Editors

引用次数: 0

Education 教育

IF 10.2 1区数学

SIAM Review Pub Date : 2022-11-03 DOI: 10.1137/22n975585

Darinka Dentcheva

{"title":"Education","authors":"Darinka Dentcheva","doi":"10.1137/22n975585","DOIUrl":"https://doi.org/10.1137/22n975585","url":null,"abstract":"SIAM Review, Volume 64, Issue 4, Page 1029-1029, November 2022. <br/> This issue of SIAM Review contains two papers in the Education section. The first, “A Generalized Dual Transform: Linear Algebra and Geometry of (Pseudo)Inverting a Matrix,” is presented by L. P. Withers, Jr. For a linear subspace $A$ of a vector space $V$, we may have a nonorthogonal basis of $A$. We could obtain an orthogonal basis (e.g., by the Gram--Schmidt orthogonalization procedure) and the orthogonality helps us to represent each element $bin A$ as a linear combination of the new basis in an easy way. How should we express $b$ as a linear combination of the original, unorthogonalized vectors? One suggestion is to construct a complementary list of vectors, called a dual list, such that each pair of vectors $a^i,a^j$ on that list are orthogonal and each vector has a length of one. The construction is called the dual transform. Involving the complementary subspace of $A$ in $V$ and orthogonal projections, we obtain again a simple formula for the representation of $b$. Next to generating dual vectors, the Gram--Schmidt orthogonalization procedure exhibits other interesting properties, which lead to a parallel so-called butterfly process for computing the dual transform. The article proceeds to explain how the dual transform is generalized via axioms and how the respective procedures are performed in the general setting. Several examples supplement the discussion. The paper is accessible to advanced undergraduate students with basic knowledge in linear algebra and complex analysis. The second article, “When Randomness Helps in Undersampling,” was written by Roel Snieder and Michael B. Wakin. In our digital era, we use many recordings: music, sounds of nature, and others. Many other signals such as telecommunication, temperature, and air pressure, are recorded for practical and scientific purposes. When signals are stored in computers, they are digitized by collecting and storing values of some functions at discrete times. A straightforward thought on how to accomplish that is to collect values uniformly in time and in all frequency components. However, the measurements might be feasible only for some times or frequencies; otherwise data acquisition or data transmission of a full collection might be too burdensome. When some times or frequencies are left out, it is said that the signal is undersampled. In that case, it is best to choose the times or frequencies to be left out randomly instead of uniformly. The authors focus on the problem of reconstructing a signal in the time domain using undersampled frequency components. The benefits of random undersampling are illustrated with an example of the air pressure recorded at a volcano in Costa Rica, but the authors cite other sources on seismic surveys as well as magnetic resonance imaging where benefits from undersampling are evidenced. The key to understand the phenomena is to analyze the effect of the sampling on the discret","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"19 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138534673","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 : 2022-11-03 DOI: 10.1137/22n975561

Misha E. Kilmer

{"title":"Research Spotlights","authors":"Misha E. Kilmer","doi":"10.1137/22n975561","DOIUrl":"https://doi.org/10.1137/22n975561","url":null,"abstract":"SIAM Review, Volume 64, Issue 4, Page 919-919, November 2022. <br/> The first Research Spotlights article in this issue is concerned with filtering, a task of paramount importance in a great many applications such as numerical weather prediction and geophysical data assimilation. Authors Alessio Spantini, Ricardo Baptista, and Youssef M. Marzouk, in their article “Coupling Techniques for Nonlinear Ensemble Filtering,” describe discrete-time filtering as the act of characterizing the sequence of conditional distributions of the latent field at observation times, given all currently available measurements. Despite the existing literature on filtering, issues such as high-dimensional state spaces and sparse (in both space and time) observations still prove formidable in practice. The traditional approach of ensemble-based data assimilation is the ensemble Kalman filter (EnKF), involving a prediction (forecasting) step followed by an analysis step. However, the authors note an intrinsic bias of EnKF due to the linearity of the transformation, estimated under Gaussian assumptions, that is used in the analysis step, which limits its accuracy. To overcome this, they propose two non-Gaussian generalizations of the EnKF---the so-called stochastic and deterministic map filters---using nonlinear transformations derived from couplings between the forecast distribution and the filtering distribution. What is crucial is that the transformations “can be estimated efficiently...perhaps using only convex optimization,” that they “are easy to `localize' in high dimensions,” and that their computation “should not become increasingly challenging as the variance of the observation noise decreases.” Following a comprehensive description of their new approaches, the authors demonstrate numerically the superiority of their stochastic map filter approach over traditional EnKF. The subsequent discussion offers the reader several jumping off points for future research. Recovery of a sparse solution to a large-scale optimization problem is another ubiquitous problem arising in many applications such as image reconstruction, signal processing, and machine learning. The cost functional typically includes a regularization term in the form of an $ell_1$ norm term on the solution and/or regularized solution to enforce sparsity. Designing suitable algorithms for such recovery problems is the subject of our second Research Spotlights article. In “Sparse Approximations with Interior Point Methods,” authors Valentina De Simone, Daniela di Serafino, Jacek Gondzio, Spyridon Pougkakiotis, and Marco Viola set out to correct the misconception that first-order methods are to be preferred over second-order methods out of hand. Through case studies, they offer evidence that interior point methods (IPMs) which are constructed to “exploit special features of the problems in the linear algebra of IPMs” and which are designed “to take advantage of the expected sparsity of the optimal solution” ","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"11 1","pages":""},"PeriodicalIF":10.2,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138534655","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

A Proximal Markov Chain Monte Carlo Method for Bayesian Inference in Imaging Inverse Problems: When Langevin Meets Moreau 成像反问题中贝叶斯推理的近端马尔可夫链蒙特卡罗方法:当Langevin遇到Moreau时

IF 10.2 1区数学

SIAM Review Pub Date : 2022-11-01 DOI: 10.1137/22m1522917

Alain Durmus, É. Moulines, M. Pereyra

引用次数: 7

A Generalized Dual Transform: Linear Algebra and Geometry of (Pseudo)Inverting a Matrix 广义对偶变换:矩阵(伪)逆的线性代数与几何

IF 10.2 1区数学

SIAM Review Pub Date : 2022-11-01 DOI: 10.1137/19m1270410

L. Withers

引用次数: 0

When Randomness Helps in Undersampling 当随机性有助于欠采样时