Research
We develop algorithms and software for efficient numerical computation, with an emphasis on tensor algebra, matrix computations, and parallel computing.
Tensor algebra
Multidimensional data in scientific computing and machine learning can be represented as tensors. We study dense and sparse tensor algebra, tensor decompositions, and tensor networks, including their algorithms, numerical methods, and software abstractions.
Matrix computations
Numerical linear algebra underlies many computational approaches in the data sciences. We develop fast matrix algorithms for nonlinear optimization, low-rank approximation, and eigenvalue problems.
Quantum systems
Tensor representations provide a way to model quantum entanglement. We investigate parallel numerical algorithms for quantum chemistry, including electronic structure calculations, and for quantum circuit simulation.
Communication-avoiding algorithms
Data movement through memory and across networks constrains performance and scalability. We design parallel algorithms that reduce communication volume and message counts for tensor computations, graph problems, parallel sorting, and bioinformatics.
High-performance numerical libraries
We connect algorithm development with applications through general and scalable parallel library routines.
Research opportunities and contact
For inquiries about research opportunities or collaboration, contact Edgar Solomonik at solomon2@illinois.edu.
Research support
Members
We are part of the scientific computing group at the University of Illinois Urbana-Champaign.
Faculty
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Edgar Solomonik
Associate Professor
Postdoctoral researchers
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Maryam Dehghan
Postdoctoral Researcher
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Tong Ding
Postdoctoral Researcher
PhD students
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Jack Weinstein
PhD Student in Computer Science
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Qizhao Huang
PhD Student in Computer Science
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Zhanrui Zhang
PhD Student in Computer Science
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Nick Koskelo
PhD Student in Computer Science
Master’s students
- Akhilesh Mocharla
Undergraduate students
- Sreehaas Chinnala
Publications
Publications by LPNA members and collaborators.
See also Edgar Solomonik’s complete publication list.
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Simultaneous matrix multiplication by tensor contraction aggregation.
arXiv:2610.26563 [math.NA], October 2026.
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Efficient Tensor Completion Algorithms for Highly Oscillatory Operators.
Numerical Linear Algebra with Applications 33(4), e70098, 2026.
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Simulating Clifford circuits with Gaussian elimination.
arXiv preprint arXiv:2511.06127, 2025.
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Sparse LDL, LU, and inverse butterfly factorization via tree decomposition.
arXiv preprint arXiv:2504.20305, 2025.
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Communication lower bounds for nested bilinear algorithms via rank expansion of Kronecker products.
Foundations of Computational Mathematics 25(1), 55–101, 2025.
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Tensor rank and other multipartite entanglement measures of graph states.
Physical Review A 110(3), 032409, 2024.
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Quantum 8, 1580, 2024.
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Minimum cost loop nests for contraction of a sparse tensor with a tensor network.
ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 169–181, June 2024.
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Optimizing distributed tensor contractions using node-aware processor grids.
Lecture Notes in Computer Science, Euro-Par, August 2023.
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arXiv:2307.03307 [cs.DC], July 2023.
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Alternating Mahalanobis distance minimization for accurate and well-conditioned CP decomposition.
SIAM Journal on Scientific Computing 45(6), A2781–A2812, 2023.
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Application performance modeling via tensor completion.
ACM/IEEE Supercomputing Conference, November 2023.
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Optimal round and sample-size complexity for partitioning in parallel sorting.
ACM Symposium on Parallelism in Algorithms and Architectures, June 2023.
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Cost-efficient Gaussian tensor network embeddings for tensor-structured inputs.
Conference on Neural Information Processing Systems, 2022.
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ATD: Augmenting CP tensor decomposition by self supervision.
Conference on Neural Information Processing Systems, 2022.
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Efficient preconditioners for interior point methods via a new Schur-complement-based strategy.
SIAM Journal on Matrix Analysis and Applications 43(4), 1680–1711, 2022.
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Journal of Parallel and Distributed Computing 169, 269–285, 2022.
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Accelerating alternating least squares for tensor decomposition by pairwise perturbation.
Numerical Linear Algebra with Applications 29(4), e2431, 2022.
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Parallel minimum spanning forest computation using sparse matrix kernels.
Proceedings of the SIAM Conference on Parallel Processing for Scientific Computing, February 2022.
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Fast and accurate randomized algorithms for low-rank tensor decompositions.
Conference on Neural Information Processing Systems, 2021.
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MTC: Multiresolution tensor completion from partial and coarse observations.
ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2021.
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SIAM Journal on Scientific Computing 43(4), C290–C311, 2021.
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Accelerating distributed-memory autotuning via statistical analysis of execution paths.
IEEE International Parallel and Distributed Processing Symposium, May 2021.
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Efficient parallel CP decomposition with pairwise perturbation and multi-sweep dimension tree.
IEEE International Parallel and Distributed Processing Symposium, May 2021.
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Efficient 2D tensor network simulation of quantum systems.
ACM/IEEE Supercomputing Conference, November 2020.
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AutoHOOT: Automatic High-Order Optimization for Tensors.
International Conference on Parallel Architectures and Compilation Techniques, October 2020.
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Derivation and analysis of fast bilinear algorithms for convolution.
SIAM Review 62(4), 743–777, 2020.
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On stability of tensor networks and canonical forms.
arXiv:2001.01191 [math.NA], January 2020.
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Communication-avoiding CholeskyQR2 for rectangular matrices.
IEEE International Parallel and Distributed Processing Symposium, May 2019.
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Communication-avoiding parallel algorithms for solving triangular systems of linear equations.
IEEE International Parallel and Distributed Processing Symposium, 2017.
Alumni and past participants
Postdoctoral researchers
- Raghavendra Kanakagiri, 2021–2023.
PhD alumni
- Yuchen Pang (2026)
Simulating and Analyzing Quantum Computation using Tensor Networks. - Navjot Singh (2025)
Algorithms and software for tensor decompositions. - Edward Hutter (2024)
Accelerated performance modeling and tuning of parallel programs. - Linjian Ma (2023)
Towards efficient algorithms and systems for tensor decompositions and tensor networks. - Samah Karim (2022)
Inexact interior point methods for constrained convex quadratic optimization problems.
Master’s theses
- Wentao Yang (2022)
Optimal round and sample-size complexity for partitioning in parallel sorting. - Navjot Singh (2020)
Parallel Gauss-Newton method for CP decomposition. - Tobias Wicky (2017)
A communication-avoiding algorithm for solving linear systems of equations with selective inversion.
Bachelor’s theses
Yiqing Zhou (2020), Tianyi Hao (2020), Youcef Hadjarab (2020), Zecheng Zhang (2019), Pavle Simonovic (2018), and Edward Hutter (2017).
Other past participants
Former graduate and undergraduate researchers and visitors.
- Jessica Williams
- Sreevardhan Atyam (CS and Physics)
- Aniket Deshpande (Physics)
- Anitej Chanda (CS)
- Boyang Li (CS & Math)
- Aarnav Varanasi (Physics)
- Chandani Grover (CS), 2024–2025
- Bangyan Shi (CS), 2023–2024
- Aniruddha Sen (visiting from UMass), summer 2023
- Mengyuan (Mina) Sun (CS), 2021–2023
- Changsheng Chen (CS), 2021–2023
- Tim Baer (CS), 2019–2022
- Raul Platero (CS), 2017–2021
- Dipro Ray (CS), 2019–2021
- Annika Dugad (academic visitor), 2019–2020
- Caleb Ju (CS), 2018–2020
- Yifan Zhang (Math, Engineering Physics, and Statistics), 2019–2020
- Zhaoyu Wu (CS), 2018–2019
- Hung Woei Neoh (Math & CS), 2018–2019
- Hongru Yang (CS & Statistics), 2018–2019
- Yunxin (David) Zhang (CS), 2018–2019
- Xiaoxiao Wu, 2018–2019
- Siyuan Zhang, 2018–2019
- Naijing Zhang, 2017–2019
- Fan Huang, 2018
- Eric Song, 2018
- Ruiqian Yao, 2018
- Eduardo Yap, 2018
- Peter Tatkowski, 2018
- Qile Zhi, 2017
- Thomas Warther, 2017
Courses and recorded lectures
Recent courses
- Numerical Analysis, CS 450, Fall 2026.
- Parallel Numerical Algorithms, CS 554, Spring 2026. Fall 2023 course materials.
- Tensor Computations, CS 598-EVS, Fall 2024.
Lecture and course archive
- Workshop on Sparse Tensor Computations — participant talks, UIUC/Chicago, October 2023.
- Efficient Inexact Solvers in Numerical Optimization Methods — E-NLA lecture by Edgar Solomonik, October 2021.
- Tensor Computations — CS 598-EVS, Spring 2022.
- Numerical Analysis — CS 450, Spring 2021.
- Parallel Numerical Algorithms — CS 554, Fall 2017.
- Basics of tensors — LPNA lecture by Edgar Solomonik, June 2017.
- Basics of communication complexity — LPNA lecture by Edgar Solomonik, June 2017.
- Communication Cost Analysis of Algorithms — CS 598-EVS, Fall 2016.