图 书 馆
从线性到非线性n宽度：简化建模中的最优性From linear to nonlinear n-width : optimality in reduced modelling |
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| 课程网址: | https://videolectures.net/8ecm2021_cohen_from_linear/ |
| 主讲教师: | Albert Cohen |
| 开课单位: | 8ECM会议 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The concept of n-width has been introduced by Kolmogorov as a way of measuring the size of compact sets in terms of their approximability by linear spaces. From a numerical perspective it may be thought as a benchmark for the performance of algorithms based on linear approximation. In recent years this concept has proved to be highly meaningful in the analysis of reduced modeling strategies for complex physical problems described by parametric problems. This lecture will first review two significant results in this area that concern (i) the practical construction of optimal spaces by greedy algorithms and (ii) the preservation of the rate of decay of widths under certain holomorphic transformation. It will then focus on recent attempts to propose non-linear version of n-widths, how these notions relate to metric entropies, and how they could be relevant to practical applications. |
| 关 键 词: | 非线性宽度; 简化建模; 最优性 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2024-05-28：liyq |
| 最后编审: | 2024-05-28：liyq |
| 阅读次数: | 6 |