Tensor Algebra: Multidimensional data (ubiquitous in scientific computing and machine learning) can be effectively treated via tensor abstractions.
Tensors and their decompositions provide numerical tools for hypergraph processing, high-order methods, and neural networks.
Matrix Computations: Numerical linear algebra underlies most computational approaches in data sciences.
Fast matrix algorithms provide solutions for nonlinear optimization, low-rank approximation, and eigenvalue problems.
Quantum Systems: Tensor representations provide the most natural way to computationally model entanglement (correlation between electrons).
We investigate numerical parallel algorithms for tensor computations arising in quantum chemistry (e.g. high-accuracy electronic structure calculations) and quantum information (e.g. quantum circuit simulation).
Communication Complexity: Performance and scalability of algorithms and libraries is constrained by data movement in the memory hierarchy and network.
We aim to design parallel algorithms that minimize the amount of communication and number of messages.
High Performance Numerical Libraries: Parallel numerical libraries are the glue between fast algorithms and real-world applications.
We pursue application-driven research on algorithms by way of developing general and scalable library routines.
(Dec 2018) Edward Hutter is one of two UIUC PhD students in the DOE CSGF class of 2018 (CS @ Illinois news article).
(Nov 2018) Edgar Solomonik is one of three winners of the 2018 IEEE TCHPC Award for Excellence in Early Career Research, also see CS @ Illinois news article.
(May 2018) Congratulations to Pavle Simonovic (completed BS thesis) and Peter Tatkowski (joining ETH Zurich MS program)!
(May 2018) Congratulations to Qile Zhi for winning the Franz Hohn and J.P. Nash Scholarship.
(March 2018) See Edward Hutter's presentation on Cholesky-QR2 at SIAM PP 2018 in Tokyo (slides).
(July 2017) Congratulations to Raul Platero for being a winner of the Outstanding Oral Presentation prize at the 2017 Illinois Summer Research Symposium (ISRS)!
(June 2017) Congratulations to Tobias Wicky for finishing his MS thesis and to Edward Hutter for finishing his BS thesis!
(June 2017) Group webpage is up, welcome!
We are always looking for new collaborators and participants. If you are a UIUC student interested in doing research in the area, email Edgar Solomonik (solomon2@illinois.edu).
web-course Numerical analysis Spring 2018, Fall 2018; CS 450
web-course Parallel numerical algorithms Fall 2017; CS 554
video June 2017; LPNA Lecture; Basics of tensors (Edgar)
video June 2017; LPNA Lecture; Basics of communication complexity (Edgar)
web-course Communication cost analysis of algorithms Fall 2016; CS 598-ES
report | Linjian Ma and Edgar Solomonik Accelerating Alternating Least Squares for Tensor Decomposition by Pairwise Perturbation> arXiv:1811.10573 [math.NA], November 2018. |
report | Edward Hutter and Edgar Solomonik Communication-avoiding Cholesky-QR2 for rectangular matrices arXiv:1710.08471 [cs.DC], October 2017. |
article | Tobias Wicky, Edgar Solomonik, and Torsten Hoefler Communication-avoiding parallel algorithms for solving triangular systems of linear equations IEEE International Parallel and Distributed Processing Symposium (IPDPS), Orlando, FL, June 2017, pp. 678-687. report |