Research
My research develops algorithms and software for numerical linear algebra and tensor computations, with an emphasis on reducing computation and communication costs. I work on parallel algorithms, tensor contraction and decomposition, fast matrix multiplication, quantum simulation, and graph algorithms.
I lead the Laboratory for Parallel Numerical Algorithms (LPNA).
Teaching
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CS 450: Numerical Analysis
Current: Fall 2026.
Previously: Spring 2018, Fall 2018, Spring 2021, Spring 2023, Spring 2024.
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CS 554: Parallel Numerical Algorithms
Spring 2026; Fall 2017, Fall 2019, Fall 2021, Fall 2023.
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CS 598: Tensor Computations
Fall 2024; Fall 2020, Spring 2022.
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CS 357: Numerical Methods
Spring 2017.
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Software
Cyclops Tensor Framework
Algebraic parallel programming with distributed tensors.
CANDMC
Distributed-memory matrix factorization algorithms.
See also Cyclops community software and my GitHub page.
Contact
solomon2@illinois.edu4229 Thomas M. Siebel Center for Computer Science
201 North Goodwin Avenue
Urbana, IL 61801-2302
217-300-4794
Fellowships and awards
- Presidential Early Career Award for Scientists and Engineers (PECASE), 2025.
- Jack Dongarra Early Career Award, 2024.
- C.W. Gear Outstanding Junior Faculty Award, 2022.
- Dean’s Award for Excellence in Research, 2021.
- NSF CAREER Award, 2020.
- SIAM Activity Group on Supercomputing Early Career Prize, 2020.
- IEEE TCHPC Early Career Researchers Excellence Award in High Performance Computing, 2018.
- Alston S. Householder Prize XX, 2017.
- ETH Zurich Postdoctoral Fellowship, 2014–2016.
- David J. Sakrison Memorial Prize, 2014.
- NERSC Award for Innovative Use of High Performance Computing, 2013.
- ACM/IEEE-CS George Michael Memorial High Performance Computing Fellowship, 2013.
- DOE Computational Science Graduate Fellowship, 2010–2014.
Background
- Postdoctoral Fellow, ETH Zurich, 2014–2016.
- Ph.D. in Computer Science, University of California, Berkeley, 2014. Advisor: James W. Demmel.
- B.S. in Computer Science, University of Illinois Urbana-Champaign, 2010.
Publications and preprints
The list follows my CV. Selected publications have a red link and a “Selected” label. See the LPNA website for further work by the group.
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Simultaneous matrix multiplication by tensor contraction aggregation.
arXiv:2610.26563 [math.NA], October 2026.
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Accelerating Galerkin reduced-order models for turbulent flows with tensor decomposition.
SIAM Journal on Scientific Computing, accepted for publication.
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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.
preprint Selected -
Sparse LDL, LU, and inverse butterfly factorization via tree decomposition.
arXiv preprint arXiv:2504.20305, 2025.
preprint Selected -
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.
article Selected -
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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Accelerating sparse data orchestration via dynamic reflexive tiling.
ACM International Conference on Architectural Support for Programming Languages and Operating Systems, March 2023.
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SciPost Physics Codebases 10, February 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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Communication lower bounds of bilinear algorithms for symmetric tensor contractions.
SIAM Journal on Scientific Computing 43(5), A3328–A3356, 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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Fast bilinear algorithms for symmetric tensor contractions.
Computational Methods in Applied Mathematics 21(1), 211–231, 2021.
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Efficient 2D tensor network simulation of quantum systems.
ACM/IEEE Supercomputing Conference, November 2020.
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Distributed-memory DMRG via sparse and dense parallel tensor contractions.
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-efficient Jaccard similarity for high-performance distributed genome comparisons.
IEEE International Parallel and Distributed Processing Symposium, May 2020.
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ExTensor: An accelerator for sparse tensor algebra.
IEEE/ACM International Symposium on Microarchitecture, October 2019.
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ACM Symposium on Parallelism in Algorithms and Architectures, June 2019.
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Communication-avoiding CholeskyQR2 for rectangular matrices.
IEEE International Parallel and Distributed Processing Symposium, May 2019.
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Scaling betweenness centrality using communication-efficient sparse matrix multiplication.
ACM/IEEE Supercomputing Conference, November 2017.
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Pareto-efficient quantum circuit simulation using tensor contraction deferral.
arXiv:1710.05867 [quant-ph], October 2017.
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A communication-avoiding parallel algorithm for the symmetric eigenvalue problem.
ACM Symposium on Parallelism in Algorithms and Architectures, 2017.
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To push or to pull: on reducing communication and synchronization in graph computations.
26th ACM Symposium on High Performance Parallel and Distributed Computing, Washington DC, 2017.
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Communication-avoiding parallel algorithms for solving triangular systems of linear equations.
IEEE International Parallel and Distributed Processing Symposium, 2017.
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SlimSell: A vectorizable graph representation for breadth-first search.
IEEE International Parallel and Distributed Processing Symposium, 2017.
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ACM Transactions on Parallel Computing 3(1), Article 3, 2016.
article Selected -
Sparse tensor algebra as a parallel programming model.
arXiv:1512.00066 [cs.MS], 2015.
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A massively parallel tensor contraction framework for coupled-cluster computations.
Journal of Parallel and Distributed Computing 74(12), 3176–3190, 2014.
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ACM Symposium on Parallelism in Algorithms and Architectures, 2014.
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Reconstructing Householder vectors from Tall-Skinny QR.
IEEE International Parallel and Distributed Processing Symposium, 2014.
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IEEE International Parallel and Distributed Processing Symposium, 2013.
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Minimizing communication in all-pairs shortest paths.
IEEE International Parallel and Distributed Processing Symposium, 2013.
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A communication-optimal n-body algorithm for direct interactions.
IEEE International Parallel and Distributed Processing Symposium, 2013.
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Matrix multiplication on multidimensional torus networks.
Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2013.
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Communication avoiding and overlapping for numerical linear algebra.
ACM/IEEE Supercomputing Conference, 2012.
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A preliminary analysis of Cyclops Tensor Framework.
Technical Report UCB/EECS-2012-29, University of California, Berkeley, 2012.
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Improving communication performance in dense linear algebra via topology aware collectives.
ACM/IEEE Supercomputing Conference, 2011.
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Communication-optimal parallel 2.5D matrix multiplication and LU factorization algorithms.
Lecture Notes in Computer Science, Euro-Par, 2011.
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Encyclopedia of Parallel Computing, Springer, David Padua, Ed., 2011.
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International Journal of High Performance Computing Applications 24(4), 411–427, 2010.
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Highly scalable parallel sorting.
IEEE International Parallel and Distributed Processing Symposium, 2010.
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Workshop on Parallel Programming Patterns, 2010.
Doctoral dissertation
Edgar Solomonik. Provably efficient algorithms for numerical tensor algebra. University of California, Berkeley, August 2014.
Talks and slides
Selected slides from 2010–2026.
- slides July 2, 2026; Saint-Girons Conference; Sparse LDL, LU, and Inverse Butterfly Factorization via Tree Decomposition
- slides July 31, 2025; SIAM Annual Meeting; Montreal, Canada; Contracting Tensor Networks from Clifford Circuits Using GF(2) Gaussian Elimination
- slides May 2024; ISC High Performance; Hamburg, Germany; High Performance Tensor Network Contraction and Decomposition Algorithms
- slides January 2024; Lehigh University; Optimization Methods for Tensor Decomposition
- slides March 2023; SIAM CSE; Amsterdam, NL; Faster Accurate Sketching for Tensor Networks
- slides September 2022;Scaling Numerical Algorithms and Software via Improved Performance Modeling; ICL seminar, University of Tennessee
- slides September 2022; Efficient Algorithms via Inexact Linear Solvers and Randomized Sampling; SIAM ACDA Workshop CAES-CNRS
- slides May 2022; CECAM Workshop on Quantum Chemistry Methods for Materials Science; Tensor Software and Algorithms for Quantum Chemistry
- slides December 2021; MolSSI Workshop on HPC in Computational Chemistry and Materials Science; Tensor Algorithms and Libraries for Quantum Chemistry and Materials Science
- slides October 2021; E-NLA seminar; Efficient Inexact Solvers in Numerical Optimization Methods
- slides July 2021; SIAM Annual Meeting; Communication Lower Bounds for Bilinear Algorithms
- slides May 2021; Quantum Information for Mathematics, Economics, and Statistics; IMSI, IL USA; Tensor Optimization Libraries and Algorithms for Quantum Simulation
- slides March 2021; SIAM CSE; New Methods and Software for Tensor Computations
- slides February 2021; Fast Code seminar; Scalable Algorithms for Tensor Computations
- slides October 2020; SPCL_Bcast(COMM_WORLD) seminar; High Performance Tensor Computations
- slides July 2020; IQUIST seminar; UIUC Tensor Algorithms and Software on Quantum Simulation
- slides February 2020; SIAM PP; Seattle WA, USA; Scalable Algorithms for Tensor Computations
- slides December 2019; University of Utah; Utah, USA; Scalable Algorithms for Tensor Computations
- slides March 2019; SIAM CSE; Spokane WA, USA; Accelerating Alternating Least Squares for Tensor Decomposition by Pairwise Perturbation
- slides January 2019; Invited Workshop on Compiler Techniques for Sparse Tensor Algebra; Cambridge MA, USA; Scalable Tensor Computations with Cyclops and Faster Algorithms for Alternating Least Squares
- slides January 2019; Enabling Quantum Leap: Quantum algorithms for quantum chemistry and materials; Alexandria VA, USA; Classical Computer Science and Quantum Computing: High Performance Computing and Quantum Simulation
- slides November 2018; Conference on Sparse Direct Solvers; Purdue; Lafayette IN, USA; Communication-avoiding factorization algorithms
- slides demo July 2018; PASC; Basel, Switzerland; Parallel Tensor Computations in Python or C++ Using Cyclops
- slides demo June 2018; PMAA keynote talk; Zurich, Switzerland; Scalable Tensor Algorithms for Scientific Computing
- slides March 2018; American Chemical Society (ACS) Annual Meeting; New Orleans LA, USA; Scalable Quantum Chemistry with Cyclops
- slides Nov 2017; Supercomputing; Denver CO, USA; Scaling betweenness centrality using communication-efficient sparse matrix multiplication
- slides Oct 2017; Seminar; Argonne National Laboratory; Argonne IL, USA; A massively parallel library for matrix and tensor algorithms
- slides Sep 2017; Theory Seminar; University of Illinois at Urbana-Champaign; Urbana IL, USA; Strassen-like algorithms for symmetric tensor contractions
- slides demo Sep 2017; Simons CCQ Tensor Network Workshop; New York NY, USA; Leveraging sparsity and symmetry in parallel tensor contractions
- slides July 2017; SPAA; Washington DC, USA; A communication-avoiding parallel algorithm for the symmetric eigenvalue problem
- slides June 2017; Householder prize lecture; Blacksburg VA, USA; Towards an algebraic formalism for scalable numerical algorithms
- slides June 2017; Householder Symposium XX; Blacksburg VA, USA; A communication-avoiding parallel algorithm for the symmetric eigenvalue problem
- slides May 2017; Illinois Data Science Fundamentals Summit; Urbana IL, USA; Scalable numerical linear algebra for data science
- 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
- slides April 2017; Scientific and Statistical Computing Seminar; University of Chicago; Chicago IL, USA; Strassen-like algorithms for symmetric tensor contractions
- slides March 2017; Theory Seminar; University of Illinois at Urbana-Champaign; Urbana IL, USA; Communication cost models and a few lower and upper bounds
- slides February 2017; SIAM CSE; Atlanta GA, USA; A distributed memory library for sparse tensor functions and contractions
- slides July 2016; ISTCP; Grand Forks ND, USA; Developing scalable and portable electronic structure methods with Cyclops Tensor Framework
- slides April 2016; Charm++ Workshop; University of Illinois at Urbana-Champaign; Urbana IL, USA; A parallel library for multidimensional array computations with runtime tuning
- slides April 2016; SIAM PP; Paris, France; Low rank bilinear algorithms for symmetric tensor contractions
- slides March 2016; University of California, Davis; Davis CA, USA; Provably efficient algorithms for multilinear algebra
- slides March 2016; University of Toronto; Toronto ON, Canada; Algorithms as multilinear tensor equations
- slides March 2016; University of Illinois at Urbana-Champaign; Urbana IL, USA; Algorithms as multilinear tensor equations
- slides March 2016; Stony Brook University; Stony Brook NY, USA; Algorithms as multilinear tensor equations
- slides February 2016; California Institute of Technology; Pasadena CA, USA; Algorithms as multilinear tensor equations
- slides February 2016; University of Colorado, Boulder; Boulder CO, USA; Algorithms as multilinear tensor equations
- slides February 2016; Georgia Institute of Technology; Atlanta GA, USA; Algorithms as multilinear tensor equations
- slides February 2016; Cornell University; Ithaca NY, USA; Provably efficient algorithms as tensor equations
- slides January 2016; TU München; Munich, Germany; Algorithms as multilinear tensor equations
- slides December 2015; Guest Lecture; Design of Parallel and High-Performance Computing; ETH Zurich, Switzerland; Distributed-memory models and algorithms
- slides November 2015; MATHICSE Institute Seminar; EPFL; Lausanne, Switzerland; Provably efficient algorithms for tensor computations
- slides October 2015; SIAM LA; Atlanta GA, USA; Minimizing communication in tensor contraction algorithms
- slides October 2015; DMML; Berkeley CA, USA; Communication lower bounds for numerical tensor algebra
- slides June 2015; QESC; Kobe, Japan; Efficient tensor contraction algorithms for coupled cluster
- slides February 2015; Max-Planck-Institute for Chemical Energy Conversion; Mülheim, Germany; Efficient algorithms for tensor contractions in coupled-cluster
- slides December 2014; Guest Lecture; Design of Parallel and High-Performance Computing; ETH Zurich, Switzerland; Distributed-memory models and algorithms
- slides August 2014; Dissertation talk; Berkeley CA, USA; Provably efficient algorithms for numerical tensor algebra
- slides July 2014; DOE CSGF Program Review; Washington DC, USA; Minimizing communication in numerical linear algebra
- slides June 2014; SPAA; Prague, Czech Republic; Tradeoffs between synchronization, communication, and computation in parallel linear algebra computations
- slides June 2014; ETH Zurich, Switzerland; Algorithms for contraction of tensors over a commutative ring
- slides June 2014; Householder Symposium XIX; Spa, Belgium; Contracting symmetric tensors via fully-symmetric intermediates
- slides Feb 2014; LBNL, Berkeley, CA; Cyclops Tensor Framework
- slides Feb 2014; SIAM PP; Portland, OR; Tradeoffs between synchronization, communication, and work in parallel linear algebra computations
- slides Feb 2014; Berkeley, CA; Tradeoffs between synchronization, communication, and work in parallel schedules
- slides Feb 2014; Berkeley, CA; Fast tensor contraction algorithms for Coupled Cluster
- slides Dec 2013; Laguna Beach, CA; A distributed-memory framework for tensor contractions
- slides Dec 2013; Berkeley, USA; A framework for mapping and redistribution of multidimensional distributed arrays
- slides Oct 2013; Berkeley, USA; Communication-avoiding algorithms for dense matrix factorizations
- slides Oct 2013; Berkeley, CA; Efficient algorithms for symmetric tensor contractions
- slides June 2013; ETH Zurich; Switzerland; Communication-avoiding parallel algorithms for dense linear algebra
- slides June 2013; Swiss National Supercomputing Center; Lugano, Switzerland; Communication-avoiding parallel numerical algorithms for dense matrices and tensors
- slides May 2013; IPDPS; Boston, USA; Cyclops Tensor Framework: reducing communication and eliminating load imbalance in massively parallel contractions
- slides May 2013; IPDPS; Boston, USA; Minimizing communication in all-pairs shortest paths
- slides March 2013; SIAM CSE; Boston, USA; Scalable numerical algorithms for electronic structure calculations
- slides February 2013; Berkeley, USA; Communication-avoiding parallel algorithms for dense linear algebra and tensor computations
- slides January 2013; University of Southern California; LA, USA; A parallel tensor framework for Coupled Cluster
- slides Sep. 2012; seminar; Lawrence Livermore National Laboratory; Livermore, CA; Scalable numerical algorithms for electronic structure calculations
- slides July 2012; University of Tokyo; Tokyo, Japan; 2.5D algorithms for distributed-memory computing
- slides July 2012; VECPAR; Kobe, Japan; Matrix multiplication on multidimensional torus networks
- slides June 2012; SIAM ALA; Valencia, Spain; 2.5D Algorithms for dense linear algebra
- slides Feb. 2012; SIAM PP; Savannah, GA; Topology-aware parallel algorithms for symmetric tensor contractions
- slides Nov. 2011; ACM/IEEE Supercomputing; Seattle, WA; Improving communication performance in dense linear algebra via topology-aware collectives
- slides Sep. 2011; CS 294 lecture; Berkeley, CA; 2.5D algorithms: from hardware to theory and back
- slides Sep. 2011; Bordeaux, France; Communication-optimal parallel 2.5D matrix multiplication and LU factorization algorithms
- slides Aug. 2011; seminar; Argonne National Laboratory; Argonne, IL; Reducing communication in dense matrix/tensor computations
- slides Apr. 2010; IPDPS; Atlanta, GA; Highly scalable parallel sorting