Laboratory for Parallel Numerical Algorithms

Research Topics

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.

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.

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.

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.


(June 2016) Congratulations to Tobias Wicky for finishing his MS thesis and to Edward Hutter for finishing his BS thesis!

(June 2016) Group webpage is up, welcome!


Cyclops Tensor Framework
a distributed-memory library for graph, matrix, and tensor computations

a suite of parallel algorithms for matrix factorization and eigendecomposition


We are part of the scientific computing group at the University of Illinois at Urbana-Champaign.


Edgar Solomonik
Assistant Professor

Graduate Students

Edward Hutter
PhD Student
Raul Platero
PhD Student, supported via SPI program

Undergraduate Students

Pavle Simonovic (Math & CS)
Peter Tatkowski (CS)
Zecheng Zhang (CS)
Thomas Warther (CS)
Eric Song (CS)
Youxin (Oscar) Chen (CS)
Eduardo Yap (Eng. Phys.)


Tobias Wicky (MS 2017): A communication-avoiding algorithm for solving linear systems of equations with selective inversion

Video Lectures

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


slides July 2017; LPNA Group presentation; Urbana IL, USA; Least Squares Updating for Kronecker Products (Raul)

slides July 2017; LPNA Group presentation; Urbana IL, USA; A new tunable QR factorization algorithm (Edward)

slides May 2017; Illinois Data Science Fundamentals Summit; Urbana IL, USA; Scalable numerical linear algebra for data science (Edgar)

slides May 2017; MolSSI Workshop on Core Software Blocks in Quantum Chemistry: Tensors and Integrals; Monterey Bay CA, USA; An overview of Cyclops Tensor Framework (Edgar)


report 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, Florida, June 2017 (to appear), arXiv:1612.01855 [cs.DC], December 2016. bibtex