Basic course info

Lecturers:

• Prof. Shivkumar Chandrasekaran (main speaker - SC), ECE department, University of California Santa Barbara, Santa Barbara, CA, United States (shiv@ece.ucsb.edu)

• Dr. Nithin Govindarajan (co-lecturer), ESAT, KU Leuven, Leuven, Belgium (nithin.govindarajan@kuleuven.be)

Dates: 2 March - 11 March

Location: Huis Bethlehem, Aula Wolfspoort, Schapenstraat 34, 3000 Leuven

Prerequisites: Linear algebra, computational linear algebra

Outline

This course provides an introduction to the foundations of fast algorithms for structured matrices. After a general overview of Strassen’s method for dense matrices and algorithms for sparse matrices, the emphasis of the course will primarily be on algorithms for dense structured matrices. Two structures to be discussed in detail are: (i) the low displacement structure pioneered by Kailath et al., and (ii) the low-rank structures pioneered by Dewilde & van der Veen, Eidelman & Gohberg, Hackbusch, Rokhlin & Greengard, and others. We shall discuss the impact of these algorithms in various application domains such as fast solvers for PDEs, integral equations, problems in systems & control, and polynomial arithmetic. Both theory and algorithms will be emphasized in the course.

Course assesment

The student’s grade will be evaluated based-off their performance on the course assignments. There will be in total 3 take-home assignments which will be handed over to the students at the end of every session. These assignments contain a collection of hands-on coding exercises along with some theoretical questions.

It is recommended that the coding assignments are done in the Julia programming language environment, however the students are free to work with their preferred programming language of choice.