图 书 馆
AAA-最小二乘有理逼近和拉普拉斯问题的解AAA-least squares rational approximation and solution of Laplace problems |
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| 课程网址: | http://videolectures.net/8ecm2021_trefethen_aaa_squares/ |
| 主讲教师: | Nick Trefethen |
| 开课单位: | 牛津大学 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | In the past five years, computation with rational functions has advanced greatly with the introduction of the AAA algorithm for barycentric rational approximation and of lightning least-squares solvers for Laplace, Stokes, and Helmholtz problems. Here we combine these methods into a two-step method for solving planar Laplace problems. First, complex rational approximations to the boundary data are determined by AAA approximation, locally near each corner or other singularity. The poles of these approximations outside the problem domain are then collected and used for a global least-squares fit to the solution. Typical problems are solved in a second of laptop time to 8-digit accuracy, all the way up to the corners. This is joint work with Stefano Costa. |
| 关 键 词: | AAA算法; 最小二乘; 有理函数 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2022-03-27：hqh |
| 最后编审: | 2022-03-27：hqh |
| 阅读次数: | 31 |