An optional hypercube direct N-body solver on the connection machine. - Jean-Philippe Brunet; Alan Edelman; Jill P. Mesirov (SC, 1990)

Optimal Matrix Transposition and Bit Reversal on Hypercubes: All-to-All Personalized Communication. - Alan Edelman (J. Parallel Distributed Comput., 1991)

Large Dense Numerical Linear Algebra in 1993: the Parallel Computing Influence. - Alan Edelman (Int. J. High Perform. Comput. Appl., 1993)

Hypercube Algorithms for Direct N-Body Solvers for Different Granularities. - Jean-Philippe Brunet; Jill P. Mesirov; Alan Edelman (SIAM J. Sci. Comput., 1993)

Scaling for orthogonality. - Alan Edelman; G. W. Stewart (IEEE Trans. Signal Process., 1993)

Erratum: Hypercube Algorithms for Direct N-Body Solvers for Different Granularities. - Jean-Philippe Brunet; Alan Edelman; Jill P. Mesirov (SIAM J. Sci. Comput., 1994)

Index Transformation Algorithms in a Linear Algebra Framework. - Alan Edelman; Steve Heller; S. Lennart Johnsson (IEEE Trans. Parallel Distributed Syst., 1994)

Scalable Parallel Numerical Methods and Software Tools for Material Design. - Eric J. Bylaska; Scott R. Kohn; Scott B. Baden; Alan Edelman; Ryoichi Kawai; M. Elizabeth G. Ong; John H. Weare (PP, 1995)

On the Determinant of a Uniformly Distributed Complex Matrix. - Alan Edelman (J. Complex., 1995)

On Parlett's matrix norm inequality for the Cholesky decomposition. - Alan Edelman; Walter F. Mascarenhas (Numer. Linear Algebra Appl., 1995)

The Mathematics of the Pentium Division Bug. - Alan Edelman (SIAM Rev., 1997)

A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations. - Alan Edelman; Erik Elmroth; Bo Kågström (SIAM J. Matrix Anal. Appl., 1997)

The Geometry of Algorithms with Orthogonality Constraints. - Alan Edelman; Tomás A. Arias; Steven Thomas Smith (SIAM J. Matrix Anal. Appl., 1998)

The Future Fast Fourier Transform? - Alan Edelman; Peter McCorquodale; Sivan Toledo (SIAM J. Sci. Comput., 1998)

MITMatlab: A Tool for Interactive Supercomputing. - Parry Husbands; Charles Lee Isbell Jr.; Alan Edelman (PP, 1999)

A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm. - Alan Edelman; Erik Elmroth; Bo Kågström (SIAM J. Matrix Anal. Appl., 1999)

Staircase Failures Explained by Orthogonal Versal Forms. - Alan Edelman; Yanyuan Ma (SIAM J. Matrix Anal. Appl., 2000)

Pascal Matrices. - Alan Edelman; Gilbert Strang (Am. Math. Mon., 2004)

The bias of the MVDR beamformer outputs under diagonal loading. - Raj R. Nadakuditi; Alan Edelman (ICASSP (4), 2005)

Parallel MATLAB: Doing it Right. - Ron Choy; Alan Edelman (Proc. IEEE, 2005)

Tails of Condition Number Distributions. - Alan Edelman; Brian D. Sutton (SIAM J. Matrix Anal. Appl., 2005)

Free Probability, Sample Covariance Matrices, and Signal Processing. - N. Raj Rao; Alan Edelman (ICASSP (5), 2006)

Innovative technologies II - So What's innovative and exotic about star-P for MATLAB and other clients? - Alan Edelman (SC, 2006)

Modeling and rendering of weathered stone. - Julie Dorsey; Alan Edelman; Henrik Wann Jensen; Justin Legakis; Hans Køhling Pedersen (SIGGRAPH Courses, 2006)

The efficient evaluation of the hypergeometric function of a matrix argument. - Plamen Koev; Alan Edelman (Math. Comput., 2006)

The Star-P High Performance Computing Platform. - Alan Edelman (ICASSP (4), 2007)

Sample size cognizant detection of signals in white noise - N. Raj Rao; Alan Edelman (CoRR, 2007)

MOPS: Multivariate orthogonal polynomials (symbolically). - Ioana Dumitriu; Alan Edelman; Gene Shuman (J. Symb. Comput., 2007)

The Beta-Jacobi Matrix Model, the CS Decomposition, and Generalized Singular Value Problems. - Alan Edelman; Brian D. Sutton (Found. Comput. Math., 2008)

The Polynomial Method for Random Matrices. - N. Raj Rao; Alan Edelman (Found. Comput. Math., 2008)

Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples. - Raj Rao Nadakuditi; Alan Edelman (IEEE Trans. Signal Process., 2008)

PetaBricks: a language and compiler for algorithmic choice. - Jason Ansel; Cy P. Chan; Yee Lok Wong; Marek Olszewski; Qin Zhao; Alan Edelman; Saman P. Amarasinghe (PLDI, 2009)

Autotuning multigrid with PetaBricks. - Cy P. Chan; Jason Ansel; Yee Lok Wong; Saman P. Amarasinghe; Alan Edelman (SC, 2009)

Sturm Sequences and Random Eigenvalue Distributions. - James T. Albrecht; Cy P. Chan; Alan Edelman (Found. Comput. Math., 2009)

Visualizing Large Kronecker Graphs. - Huy N. Nguyen; Jeremy Kepner; Alan Edelman (Graph Algorithms in the Language of Linear Algebra, 2011)

Performance of sample covariance based capon bearing only tracker. - Christ D. Richmond; Robert L. Geddes; Ramis Movassagh; Alan Edelman (ACSCC, 2011)

An Efficient Partitioning Oracle for Bounded-Treewidth Graphs. - Alan Edelman; Avinatan Hassidim; Huy N. Nguyen; Krzysztof Onak (APPROX-RANDOM, 2011)

Language and compiler support for auto-tuning variable-accuracy algorithms. - Jason Ansel; Yee Lok Wong; Cy P. Chan; Marek Olszewski; Alan Edelman; Saman P. Amarasinghe (CGO, 2011)

Julia: A Fast Dynamic Language for Technical Computing - Jeff Bezanson; Stefan Karpinski; Viral B. Shah; Alan Edelman (CoRR, 2012)

Novel algebras for advanced analytics in Julia. - Viral B. Shah; Alan Edelman; Stefan Karpinski; Jeff Bezanson; Jeremy Kepner (HPEC, 2013)

Array Operators Using Multiple Dispatch: A design methodology for array implementations in dynamic languages. - Jeff Bezanson; Jiahao Chen 001; Stefan Karpinski; Viral B. Shah; Alan Edelman (ARRAY@PLDI, 2014)

Parallel prefix polymorphism permits parallelization, presentation & proof. - Jiahao Chen 001; Alan Edelman (HPTCDL@SC, 2014)

Julia: A fresh approach to parallel programming. - Alan Edelman (IPDPS, 2015)

Julia Introduction. - Alan Edelman (IPDPS Workshops, 2015)

Random Triangle Theory with Geometry and Applications. - Alan Edelman; Gilbert Strang (Found. Comput. Math., 2015)

Julia implementation of the Dynamic Distributed Dimensional Data Model. - Alexander Chen; Alan Edelman; Jeremy Kepner; Vijay Gadepally; Dylan Hutchison (HPEC, 2016)

Accelerated Convolutions for Efficient Multi-Scale Time to Contact Computation in Julia. - Alexander Amini; Berthold K. P. Horn; Alan Edelman (CoRR, 2016)

A more open efficient future for AI development and data science with an introduction to Julia. - Alan Edelman (IEEE BigData, 2017)

Julia: A Fresh Approach to Numerical Computing. - Jeff Bezanson; Alan Edelman; Stefan Karpinski; Viral B. Shah (SIAM Rev., 2017)

TabulaROSA: Tabular Operating System Architecture for Massively Parallel Heterogeneous Compute Engines. - Jeremy Kepner; Ron Brightwell; Alan Edelman; Vijay Gadepally; Hayden Jananthan; Michael Jones 001; Sam Madden 001; Peter Michaleas; Hamed Okhravi; Kevin T. Pedretti; Albert Reuther; Thomas L. Sterling; et al. (HPEC, 2018)

Random Hyperplanes, Generalized Singular Values & "What's My β?". - Alan Edelman; Yuyang Wang (SSP, 2018)

Fast computation of the principal components of genotype matrices in Julia. - Jiahao Chen 001; Andreas Noack; Alan Edelman (CoRR, 2018)

Rapid software prototyping for heterogeneous and distributed platforms. - Tim Besard; Valentin Churavy; Alan Edelman; Bjorn De Sutter (Adv. Eng. Softw., 2019)

A Differentiable Programming System to Bridge Machine Learning and Scientific Computing. - Mike Innes; Alan Edelman; Keno Fischer; Christopher Rackauckas; Elliot Saba; Viral B. Shah; Will Tebbutt (CoRR, 2019)

Generalized Physics-Informed Learning through Language-Wide Differentiable Programming. - Christopher Rackauckas; Alan Edelman; Keno Fischer; Mike Innes; Elliot Saba; Viral B. Shah; Will Tebbutt (AAAI Spring Symposium: MLPS, 2020)

Signal Enhancement for Magnetic Navigation Challenge Problem. - Albert R. Gnadt; Joseph Belarge; Aaron Canciani; Lauren Conger; Joseph Curro; Alan Edelman; Peter Morales; Michael F. O'Keeffe; Jonathan Taylor; Christopher Rackauckas (CoRR, 2020)

ACED: Accelerated Computational Electrochemical systems Discovery. - Rachel C. Kurchin; Eric Muckley; Lance Kavalsky; Vinay I. Hegde; Dhairya Gandhi; Xiaoyu Sun; Matthew Johnson; Alan Edelman; James E. Saal; Christopher Vincent Rackauckas; Bryce Meredig; Viral B. Shah; et al. (CoRR, 2020)

Oceananigans.jl: Fast and friendly geophysical fluid dynamics on GPUs. - Ali Ramadhan; Gregory LeClaire Wagner; Chris Hill; Jean-Michel Campin; Valentin Churavy; Tim Besard; Andre Souza; Alan Edelman; Raffaele Ferrari; John Marshall (J. Open Source Softw., 2020)

The GSVD: Where are the Ellipses?, Matrix Trigonometry, and More. - Alan Edelman; Yuyang Wang (SIAM J. Matrix Anal. Appl., 2020)

Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks. - Ranjan Anantharaman; Yingbo Ma; Shashi Gowda; Chris Laughman; Viral B. Shah; Alan Edelman; Christopher Rackauckas (AAAI Spring Symposium: MLPS, 2021)

High-performance symbolic-numerics via multiple dispatch. - Shashi Gowda; Yingbo Ma; Alessandro Cheli; Maja Gwózdz; Viral B. Shah; Alan Edelman; Christopher Rackauckas (ACM Commun. Comput. Algebra, 2021)

On the structure of the solutions to the matrix equation G*JG=J. - Alan Edelman; Sungwoo Jeong (CoRR, 2021)

Composing Modeling And Simulation With Machine Learning In Julia. - Chris Rackauckas; Maja Gwózdz; Anand Jain; Yingbo Ma; Francesco Martinuzzi; Utkarsh Rajput; Elliot Saba; Viral B. Shah; Ranjan Anantharaman; Alan Edelman; Shashi Gowda; Avik Pal; et al. (ANNSIM, 2022)

Mixing Implicit and Explicit Deep Learning with Skip DEQs and Infinite Time Neural ODEs (Continuous DEQs). - Avik Pal; Alan Edelman; Christopher Rackauckas (CoRR, 2022)

Bridging HPC Communities through the Julia Programming Language. - Valentin Churavy; William F. Godoy; Carsten Bauer; Hendrik Ranocha; Michael Schlottke-Lakemper; Ludovic Räss; Johannes P. Blaschke; Mosè Giordano; Erik Schnetter; Samuel Omlin; Jeffrey S. Vetter; Alan Edelman (CoRR, 2022)

Reproducibility repository for Bridging HPC Communities through the Julia Programming Language. - Valentin Churavy; William F. Godoy; Carsten Bauer; Hendrik Ranocha; Michael Schlottke-Lakemper; Ludovic Räss; Johannes P. Blaschke; Mosè Giordano; Erik Schnetter; Samuel Omlin; Jeffrey S. Vetter; Alan Edelman (Zenodo, 2022)

Continuous Deep Equilibrium Models: Training Neural ODEs Faster by Integrating Them to Infinity. - Avik Pal; Alan Edelman; Chris Rackauckas (HPEC, 2023)

Locally Regularized Neural Differential Equations: Some Black Boxes were meant to remain closed! - Avik Pal; Alan Edelman; Christopher Vincent Rackauckas (ICML, 2023)

Sum-of-Squares Bounds for Quantum Optimal Control. - Flemming Holtorf; Frank Schäfer; Julian Arnold; Christopher Rackauckas; Alan Edelman (QCE, 2023)

Performance Bounds for Quantum Control. - Flemming Holtorf; Frank Schäfer; Julian Arnold; Christopher Rackauckas; Alan Edelman (CoRR, 2023)

Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms. - Utkarsh Rajput; Valentin Churavy; Yingbo Ma; Tim Besard; Tim Gymnich; Adam R. Gerlach; Alan Edelman; Christopher Rackauckas (CoRR, 2023)

The conditional DPP approach to random matrix distributions. - Alan Edelman; Sungwoo Jeong (CoRR, 2023)

Oceananigans.jl: A model that achieves breakthrough resolution, memory and energy efficiency in global ocean simulations. - Simone Silvestri; Gregory LeClaire Wagner; Christopher Hill; Matin Raayai Ardakani; Johannes P. Blaschke; Jean-Michel Campin; Valentin Churavy; Navid C. Constantinou; Alan Edelman; John Marshall; Ali Ramadhan; Andre Souza; et al. (CoRR, 2023)

A New Upper Bound For the Growth Factor in Gaussian Elimination with Complete Pivoting. - Ankit Bisain; Alan Edelman; John Urschel (CoRR, 2023)

Fifty Three Matrix Factorizations: A Systematic Approach. - Alan Edelman; Sungwoo Jeong (SIAM J. Matrix Anal. Appl., 2023)

Dynamic Task Scheduling with Data Dependency Awareness Using Julia. - Rabab Alomairy; Felipe Tome; Julian Samaroo; Alan Edelman (HPEC, 2024)

NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia. - Avik Pal; Flemming Holtorf; Axel Larsson; Torkel E. Loman; Utkarsh Rajput; Frank Schäfer; Qingyu Qu; Alan Edelman; Chris Rackauckas (CoRR, 2024)

On a perturbation analysis of Higham squared maximum Gaussian elimination growth matrices. - Alan Edelman; John Urschel; Bowen Zhu (CoRR, 2024)

On the Limit of the Tridiagonal Model for β-Dyson Brownian Motion. - Alan Edelman; Sungwoo Jeong; Ron Nissim (CoRR, 2024)

Some New Results on the Maximum Growth Factor in Gaussian Elimination. - Alan Edelman; John Urschel (SIAM J. Matrix Anal. Appl., 2024)

Backpropagation through Back Substitution with a Backslash. - Alan Edelman; Ekin Akyürek; Yuyang Wang (SIAM J. Matrix Anal. Appl., 2024)

Performance Bounds for Quantum Feedback Control. - Flemming Holtorf; Frank Schäfer; Julian Arnold; Christopher Vincent Rackauckas; Alan Edelman (IEEE Trans. Autom. Control., 2024)

Tribute to Nick Higham. - Alan Edelman (Found. Comput. Math., 2024)

Scalable Hamming Distance Computation Using Accelerated Matrix Transformations. - Rabab Alomairy; Qinglei Cao; Hatem Ltaief; David E. Keyes; Alan Edelman (ISC, 2025)

Matrix Calculus (for Machine Learning and Beyond). - Paige Bright; Alan Edelman; Steven G. Johnson (CoRR, 2025)

Scalable higher-order nonlinear solvers via higher-order automatic differentiation. - Songchen Tan; Keming Miao; Alan Edelman; Christopher Rackauckas (CoRR, 2025)

Toward Portable GPU Performance: Julia Recursive Implementation of TRMM and TRSM. - Vicki Carrica; Maxwell Onyango; Rabab Alomairy; Evelyne Ringoot; James Schloss; Alan Edelman (CoRR, 2025)

Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraints. - Avik Pal; Alan Edelman; Christopher Rackauckas (CoRR, 2025)

Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints. - Utkarsh Utkarsh; Pengfei Cai; Alan Edelman; Rafael Gómez-Bombarelli; Christopher Vincent Rackauckas (CoRR, 2025)

Scientific Machine Learning of Chaotic Systems Discovers Governing Equations for Neural Populations. - Anthony G. Chesebro; David Hofmann; Vaibhav Dixit; Earl K. Miller; Richard H. Granger; Alan Edelman; Christopher Vincent Rackauckas; Lilianne R. Mujica-Parodi; Helmut H. Strey (CoRR, 2025)

Performant Unified GPU Kernels for Portable Singular Value Computation Across Hardware and Precision. - Evelyne Ringoot; Rabab Alomairy; Valentin Churavy; Alan Edelman (CoRR, 2025)