Gene Golub SIAM Summer School: Data Sparse Approximations and Algorithms

该项目支持美国博士生参加2017年吉恩·戈卢布工业与应用数学学会(SIAM)关于数据稀疏近似和算法的暑期学校，该暑期学校将于2017年5月29日至6月9日在德国的Akademie柏林-Schmock witz举行。有关详细信息，请访问http://www3.math.tu-berlin.de/numerik/G2S3/index.html.。这个暑期班的主题是为了观察到在商业、科学和工程领域的众多现代应用中，高效而稳定地获取、分析和处理海量数据是极其具有挑战性的。最近的数学进展表明，海量数据集及其相关函数通常只能由少量相关特征来表示或准确地逼近；也就是说，海量数据可以由稀疏特征集来表示。暑期班将让博士生接触到在数据稀疏近似领域使用的最新数学和计算技术，该项目确保来自美国院校的合格学生参与。来自几个不同数学领域的技术已经在数据稀疏表示和近似的背景下使用并继续发展。其中应用了调和分析、近似理论、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、优化或近似的结果是一个线性代数问题，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，数值线性代数和最优化领域在这一过程中发挥着关键作用。需要对这些领域有扎实的知识，才能在数据稀疏近似和算法领域取得进一步的进展。该学院将在为期两周的暑期课程中包括四门课程：第一周的两门课程将专注于稀疏表示和逼近理论以及张量方法，第二周的两门课程将处理稀疏数值线性代数以及稀疏背景下的优化方法。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。

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.