Additional resources
Prof. Shivkumar Chandrasekaran
- The ISSAC 2018 tutorial paper, the talk given at the conference, and the accompanying slides.
- Website of UCSB’s Scientific Computing Group with a link of all major publications on HSS and SSS matrices.
Books, notes, reviews, and webpages of other related researchers
- The classic book by Gene Golub and Charles Van Loan: Matrix Computations. Chapter 12 in the fourth edition contains useful introductory material on displacement rank matrices and rank structured matrices.
- Chris Umans webpage and talk of him on how to bound the exponent of matrix-matrix mulitplicaton
- Thomas Kailath and Ali H. Sayed’s SIAM review paper on Displacement rank theory, and the comprehensive monograph Fast Reliable Algorithms for Matrices with Structure on the subject
- The book on Time-Varying Systems and Computations by Patrick Dewilde and Alle-Jan van der Veen. See also Alle-Jan’s PhD thesis.
- Jianlin Xia’s webpage with references to his work on HSS matrices.
- The lecture notes of Rick Beatson and Leslie Greengard for a more pedagogical exposition on the subject.
- Raf vandebril’s webpage with references to his two-volume series on semiseparable matrices co-written together with Marc van Barel and Nicola Mastronardi.
- Wolgang Hackbusch’s book on Hierarchical Matrices.
- Joel tropp and Gunnar martinsson’s review paper on randomized techniques in numerical linear algebra.
- Tim Davis’s book and John gilbert’s course page on sparse matrices.
Papers of interest
- Two classical papers on FMM: A fast algorithm for particle simulations and Rapid solution of integral equations of classical potential theory.
- The paper: A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators by Emmanuel J. Candes, Laurent Demanet, and Lexing Ying.
- The paper describing the eigenvector basis of the DFT matrix, as briefly mentioned during the lectures.
- Interesting work from Beckermann and Townsend which puts bounds on the singular values for some important matrices of low displacement rank.
- George Heinig’s paper: Inversion of Generalized Cauchy Matrices and other Classes of Structured Matrices