Fast analysis-based algorithms

Course description

This course will be an introduction to several numerical methods known as "fast analysis-based algorithms," including fast multipole methods, butterfly algorithms, hierarchical matrix compression and fast direct solvers. These algorithms can be used to solve many of the PDEs governing classical mathematical physics, namely electromagnetics, acoustics, heat diffusion, and fluid dynamics. There are additional applications in signal processing and data analysis. Methods from potential theory, applied analysis, functional analysis, numerical linear algebra, complex analysis, and asymptotic analysis are central to the construction of almost all such algorithms.

Materials

There is no one textbook for this course. Instead, there will be continually updated lectures notes available here. These lecture notes will contain many useful references for each of the topics and algorithms covered in class. As they become relevant, original journal articles and textbooks will be listed below in the table of lecture topics.

Relevant code examples will be posted on gitlab.com/oneilm/fastalgorithms.

Grading

The grades in the course will be determined by a final project and presentation.

Announcements

Important information for the course will appear below as necessary.

• First class on September 14
• October 12 is Columbus day, class will be held on October 13 instead (at the usual time, place)

Schedule

Below is an updated list of lecture topics along with any documents that were distributed, or relevant code.