Gene Golub SIAM Summer School: Data Sparse Approximations and Algorithms

Gene Golub SIAM 暑期学校：数据稀疏近似和算法

• 批准号: 1712970
• 负责人: James Nagy
• 金额: $ 1万
• 依托单位: Emory University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712970&HistoricalAwards=false
• 关键词: Gene; Golub; SIAM; Summer; Data

This project supports the participation of U.S. based PhD students to participate in the 2017 Gene Golub Society for Industrial and Applied Mathematics (SIAM) Summer School on Data Sparse Approximations and Algorithms, which will be held at Akademie Berlin-Schmockwitz in Germany, May 29 through June 9, 2017. Detailed information can be found at http://www3.math.tu-berlin.de/numerik/G2S3/index.html. The topic of this summer school is motivated by the observation that in numerous modern applications throughout business, science and engineering, it is extremely challenging to efficiently and stably acquire, analyze, and process massive amounts of data. Recent mathematical advances have shown that massive data sets, and functions associated with them, can often be represented or accurately approximated by only a small number of relevant features; that is, massive data can be represented by a sparse set of features. The summer school will expose PhD students to recent mathematical and computational techniques used in the area of data sparse approximations, and this project ensures participation of well qualified students from U.S. based institutions.Techniques from several different mathematical fields have been used and continue to be developed in the context of data sparse representations and approximations. Among them are applied harmonic analysis, approximation theory, convex analysis, frame theory, graph theory, imaging science, inverse problems, probability theory, random matrix theory, reduced order modeling, and tensor analysis. In all applications, the outcome of the modeling, simulation, optimization, or approximation is a linear algebraic problem that encodes the underlying functions, the data, and thus also the resulting sparsity. Together with appropriately chosen regularizations and metrics or norms, a key role in the process is played by the fields of numerical linear algebra and optimization. A solid knowledge of these fields is required for working with, and making further advances in the field of data sparse approximations and algorithms. The school will consist of four courses over the two-week period of the summer school: Two courses in the first week of the school will focus on the theory of sparse representation and approximation as well as tensor methods, and two courses in the second week will deal with sparse numerical linear algebra as well as optimization methods in the sparse context. The courses will include lectures as well as computational exercises and small group projects for the participants.

该项目支持美国博士生参加 2017 年 Gene Golub 工业与应用数学学会 (SIAM) 数据稀疏近似和算法暑期学校，该活动将于 5 月 29 日至 5 月 29 日至 5 日在德国柏林施莫克维茨学院举行2017年6月9日。详细信息请参见http://www3.math.tu-berlin.de/numerik/G2S3/index.html。本次暑期学校的主题源于这样的观察：在商业、科学和工程领域的众多现代应用中，高效、稳定地获取、分析和处理大量数据极具挑战性。最近的数学进展表明，海量数据集以及与之相关的函数通常可以仅用少量相关特征来表示或准确地近似；也就是说，海量数据可以用一组稀疏的特征来表示。暑期学校将使博士生接触到数据稀疏近似领域中使用的最新数学和计算技术，该项目确保来自美国机构的高素质学生的参与。来自多个不同数学领域的技术已被使用并继续开发在数据稀疏表示和近似的背景下。其中包括应用调和分析、逼近论、凸分析、框架理论、图论、成像科学、反问题、概率论、随机矩阵理论、降阶建模和张量分析。在所有应用中，建模、模拟、优化或近似的结果都是线性代数问题，它对底层函数、数据以及由此产生的稀疏性进行编码。与适当选择的正则化和度量或规范一起，数值线性代数和优化领域在该过程中发挥着关键作用。需要对这些领域有扎实的了解，才能在数据稀疏近似和算法领域进行工作并取得进一步的进展。 学校将在为期两周的暑期学校期间包括四门课程：学校第一周的两门课程将重点关注稀疏表示和逼近理论以及张量方法，第二周的两门课程将重点关注稀疏表示和逼近理论以及张量方法。将处理稀疏​​数值线性代数以及稀疏环境中的优化方法。 这些课程将包括讲座以及为参与者提供的计算练习和小组项目。