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Scalable higher-order nonlinear solvers via higher-order automatic
differentiation
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2025
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Shubin Tan
Keming Miao
Alan Edelman
Christopher Rackauckas
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Matrix Calculus (for Machine Learning and Beyond)
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2025
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Paige Bright
Alan Edelman
Steven G. Johnson
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On the Limit of the Tridiagonal Model for $\beta$-Dyson Brownian Motion
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2024
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Alan Edelman
Sungwoo Jeong
Ron Nissim
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On a perturbation analysis of Higham squared maximum Gaussian
elimination growth matrices
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2024
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Alan Edelman
John Urschel
Bowen Zhu
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Mapping Out Phase Diagrams with Generative Classifiers
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2024
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Julian Arnold
Frank Schäfer
Alan Edelman
Christoph Bruder
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Some New Results on the Maximum Growth Factor in Gaussian Elimination
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2024
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Alan Edelman
John Urschel
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Convex Network Flows
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2024
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Theo Diamandis
Guillermo Angeris
Alan Edelman
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NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of
Nonlinear Equations in Julia
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2024
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Avik Pal
Flemming Holtorf
Axel Larsson
Torkel E. Loman
Utkarsh Azad
Frank Schaefer
Qingyu Qu
Alan Edelman
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Backpropagation through Back Substitution with a Backslash
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2024
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Alan Edelman
Ekin Akyürek
Yuyang Wang
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Continuous Deep Equilibrium Models: Training Neural ODEs Faster by Integrating Them to Infinity
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2023
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Avik Pal
Alan Edelman
Christopher Rackauckas
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Fifty Three Matrix Factorizations: A Systematic Approach
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2023
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Alan Edelman
Sungwoo Jeong
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Locally Regularized Neural Differential Equations: Some Black Boxes Were Meant to Remain Closed!
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2023
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Avik Pal
Alan Edelman
Christopher Rackauckas
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Some New Results on the Maximum Growth Factor in Gaussian Elimination
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2023
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Alan Edelman
John Urschel
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Backpropagation through Back Substitution with a Backslash
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2023
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Alan Edelman
Ekin Akyürek
Yuyang Wang
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Performance Bounds for Quantum Control
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2023
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Flemming Holtorf
Frank Schäfer
Julian Arnold
Christopher Rackauckas
Alan Edelman
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Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms
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2023
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Utkarsh Utkarsh
Valentin Churavy
Yingbo Ma
Tim Besard
Prakitr Srisuma
Tim Gymnich
Adam R. Gerlach
Alan Edelman
George Barbastathis
Richard D. Braatz
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The conditional DPP approach to random matrix distributions
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2023
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Alan Edelman
Sungwoo Jeong
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Mapping out phase diagrams with generative classifiers
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2023
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Julian Arnold
Frank Schäfer
Alan Edelman
Christoph Bruder
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Oceananigans.jl: A model that achieves breakthrough resolution, memory and energy efficiency in global ocean simulations
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2023
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Simone Silvestri
Gregory LeClaire Wagner
Christopher Hill
Matin Raayai Ardakani
Johannes Blaschke
Jean‐Michel Campin
Valentin Churavy
Navid C. Constantinou
Alan Edelman
John Marshall
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A New Upper Bound For the Growth Factor in Gaussian Elimination with Complete Pivoting
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2023
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Ankit Bisain
Alan Edelman
John Urschel
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On the structure of the solutions to the matrix equation G⁎JG = J
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2022
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Alan Edelman
Sungwoo Jeong
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Composing Modeling And Simulation With Machine Learning In Julia
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2022
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Christopher Rackauckas
Maja Gwóźdź
Anand Jain
Yingbo Ma
Francesco Martinuzzi
Utkarsh Rajput
Elliot Saba
Viral B. Shah
Ranjan Anantharaman
Alan Edelman
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On the Cartan decomposition for classical random matrix ensembles
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2022
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Alan Edelman
Sungwoo Jeong
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Continuous Deep Equilibrium Models: Training Neural ODEs faster by integrating them to Infinity
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2022
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Avik Pal
Alan Edelman
Christopher Rackauckas
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Bridging HPC Communities through the Julia Programming Language
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2022
|
Valentin Churavy
William F. Godoy
Carsten Bauer
Hendrik Ranocha
Michael Schlottke‐Lakemper
Ludovic Räss
Johannes Blaschke
Mosè Giordano
Erik Schnetter
Samuel Omlin
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High-performance symbolic-numerics via multiple dispatch
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2021
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Shashi Gowda
Yingbo Ma
Alessandro Cheli
Maja Gwóźzdź
Viral B. Shah
Alan Edelman
Christopher Rackauckas
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High-performance symbolic-numerics via multiple dispatch
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2021
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Shashi Gowda
Yingbo Ma
Alessandro Cheli
Maja Gwóźdź
Viral B. Shah
Alan Edelman
Christopher Rackauckas
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On the structure of the solutions to the matrix equation $G^*JG=J$
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2021
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Alan Edelman
Sungwoo Jeong
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High-performance symbolic-numerics via multiple dispatch
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2021
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Shashi Gowda
Yingbo Ma
Alessandro Cheli
Maja Gwóźdź
Viral B. Shah
Alan Edelman
Christopher Rackauckas
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Fifty Three Matrix Factorizations: A systematic approach
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2021
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Alan Edelman
Sungwoo Jeong
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+
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Composing Modeling and Simulation with Machine Learning in Julia
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2021
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Christopher Rackauckas
Ranjan Anantharaman
Alan Edelman
Shashi Gowda
Maja Gwóźdź
Anand Jain
Chris Laughman
Yingbo Ma
Francesco Martinuzzi
Avik Pal
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The generalized Cartan decomposition for classical random matrix ensembles
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2020
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Alan Edelman
Sungwoo Jeong
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ACED: Accelerated Computational Electrochemical systems Discovery.
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2020
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Rachel C. Kurchin
Eric S. Muckley
Lance Kavalsky
Vinay I. Hegde
Dhairya Gandhi
Xiao-Yu Sun
Matthew Johnson
Alan Edelman
James E. Saal
Christopher Rackauckas
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Universal Differential Equations for Scientific Machine Learning
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2020
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Christopher Rackauckas
Yingbo Ma
Carl Julius Martensen
Collin Warner
Kirill Zubov
Rohit Supekar
Dominic J. Skinner
Ali Ramadhan
Alan Edelman
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Circuitscape in Julia: High Performance Connectivity Modelling to Support Conservation Decisions
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2020
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Ranjan Anantharaman
Kimberly R. Hall
Viral B. Shah
Alan Edelman
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A multi-control climate policy process for a trusted decision maker
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2020
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Henri F. Drake
Ronald L. Rivest
J. M. Deutch
Alan Edelman
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Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks
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2020
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Ranjan Anantharaman
Yingbo Ma
Shashi Gowda
Chris Laughman
Viral B. Shah
Alan Edelman
Christopher Rackauckas
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The GSVD: Where are the Ellipses?, Matrix Trigonometry, and More
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2020
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Alan Edelman
Yuyang Wang
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AutoMat: Accelerated Computational Electrochemical systems Discovery
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2020
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Emil Annevelink
Rachel C. Kurchin
Eric S. Muckley
Lance Kavalsky
Vinay I. Hegde
Valentin Sulzer
Shang Zhu
Jiankun Pu
David Fariña
Matthew S. Johnson
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Universal Differential Equations for Scientific Machine Learning
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2020
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Christopher Rackauckas
Yingbo Ma
Carl Julius Martensen
Collin Warner
Kirill Zubov
Rohit Supekar
Dominic J. Skinner
Ali J. Ramadhan
Alan Edelman
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Signal Enhancement for Magnetic Navigation Challenge Problem
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2020
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Albert R. Gnadt
J. Belarge
Aaron Canciani
Glenn Carl
Lauren Conger
Joseph Curro
Alan Edelman
Peter Morales
Aaron P. Nielsen
Michael O’Keeffe
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The densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix
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2019
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Vesselin Drensky
Alan Edelman
Tierney Genoar
Raymond Kan
Plamen Koev
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Zygote: A Differentiable Programming System to Bridge Machine Learning and Scientific Computing
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2019
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Mike Innes
Alan Edelman
Keno Fischer
Christopher Rackauckas
Elliot Saba
Viral B. Shah
Will Tebbutt
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Circuitscape in Julia: High Performance Connectivity Modelling to Support Conservation Decisions
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2019
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Ranjan Anantharaman
Kimberly R. Hall
Viral B. Shah
Alan Edelman
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Circuitscape in Julia: High Performance Connectivity Modelling to Support Conservation Decisions
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2019
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Ranjan Anantharaman
Kimberly R. Hall
Viral N. Shah
Alan Edelman
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A Differentiable Programming System to Bridge Machine Learning and Scientific Computing
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2019
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Mike Innes
Alan Edelman
Keno Fischer
Christopher Rackauckas
Elliot Saba
Viral B Shah
Will Tebbutt
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On computing Schur functions and series thereof
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2018
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Cy Chan
Vesselin Drensky
Alan Edelman
Raymond Kan
Plamen Koev
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TabulaROSA: Tabular Operating System Architecture for Massively Parallel Heterogeneous Compute Engines
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2018
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Jeremy Kepner
Ron Brightwell
Alan Edelman
Vijay Gadepally
Hayden Jananthan
Michael Jones
Samuel Madden
Peter Michaleas
Hamed Okhravi
Kevin Pedretti
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Random Hyperplanes, Generalized Singular Values & “What’s My β?”
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2018
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Alan Edelman
Yuyang Wang
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Fast computation of the principal components of genotype matrices in Julia
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2018
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Jiahao Chen
Andreas Noack
Alan Edelman
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Julia: A Fresh Approach to Numerical Computing
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2017
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Stefan Karpinski
Viral B. Shah
Jeffrey Werner Bezanson
Alan Edelman
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Julia: A Fresh Approach to Numerical Computing
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2017
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Jeff Bezanson
Alan Edelman
Stefan Karpinski
Viral B. Shah
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Eigenvalue approximation of sums of Hermitian matrices from eigenvector localization/delocalization
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2017
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Ramis Movassagh
Alan Edelman
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Julia implementation of the Dynamic Distributed Dimensional Data Model
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2016
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Alexander Chen
Alan Edelman
Jeremy Kepner
Vijay Gadepally
David Hutchison
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Beyond universality in random matrix theory
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2016
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Alan Edelman
Alice Guionnet
Sandrine Péché
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Accelerated Convolutions for Efficient Multi-Scale Time to Contact Computation in Julia
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2016
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Alexander Amini
Berthold K. P. Horn
Alan Edelman
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The singular values of the GUE (less is more)
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2015
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Alan Edelman
Michael La Croix
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Condition numbers of indefinite rank 2 ghost Wishart matrices
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2015
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Ramis Movassagh
Alan Edelman
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Random Triangle Theory with Geometry and Applications
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2015
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Alan Edelman
Gilbert Strang
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Random Triangle Theory with Geometry and Applications
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2015
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Alan Edelman
Gilbert Strang
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Infinite Random Matrix Theory, Tridiagonal Bordered Toeplitz Matrices, and the Moment Problem
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2015
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Alexander Dubbs
Alan Edelman
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Random Triangle Theory with Geometry and Applications
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2015
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Alan Edelman
Gilbert Strang
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Integral geometry for Markov chain Monte Carlo: overcoming the curse of search-subspace dimensionality
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2015
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Oren Mangoubi
Alan Edelman
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Infinite Random Matrix Theory, Tridiagonal Bordered Toeplitz Matrices, and the Moment Problem
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2015
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Alexander Dubbs
Alan Edelman
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Random Triangle Theory with Geometry and Applications
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2015
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Alan Edelman
Gilbert Strang
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Infinite random matrix theory, tridiagonal bordered Toeplitz matrices, and the moment problem
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2014
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Alexander Dubbs
Alan Edelman
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Julia: A Fresh Approach to Numerical Computing
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2014
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Jeff Bezanson
Alan Edelman
Stefan Karpinski
Viral B. Shah
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Infinite random matrix theory, tridiagonal bordered Toeplitz matrices, and the moment problem
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2014
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Alexander Dubbs
Alan Edelman
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The Singular Values of the GUE (Less is More)
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2014
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Alan Edelman
Michael La Croix
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+
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Parallel Prefix Polymorphism Permits Parallelization, Presentation & Proof
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2014
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Jiahao Chen
Alan Edelman
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Array operators using multiple dispatch: a design methodology for array implementations in dynamic languages
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2014
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Jeff Bezanson
Jiahao Chen
Stefan Karpinski
Viral B. Shah
Alan Edelman
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Random matrix theory, numerical computation and applications
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2014
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Alan Edelman
Brian Sutton
Yuyang Wang
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Array Operators Using Multiple Dispatch: A design methodology for array implementations in dynamic languages
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2014
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Jeff Bezanson
Jiahao Chen
Stefan Karpinski
Viral B. Shah
Alan Edelman
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Array Operators Using Multiple Dispatch
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2014
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Jeff Bezanson
Jiahao Chen
Stefan Karpinski
Viral B. Shah
Alan Edelman
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Low-temperature random matrix theory at the soft edge
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2014
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Alan Edelman
Per‐Olof Persson
Brian Sutton
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PDF
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Eigenvalue distributions of beta-Wishart matrices
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2014
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Alan Edelman
Plamen Koev
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PDF
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THE BETA-MANOVA ENSEMBLE WITH GENERAL COVARIANCE
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2014
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Alexander Dubbs
Alan Edelman
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The Singular Values of the GUE (Less is More)
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2014
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Alan Edelman
Michael La Croix
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+
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Parallel Prefix Polymorphism Permits Parallelization, Presentation & Proof
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2014
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Jiahao Chen
Alan Edelman
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+
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Julia: A Fresh Approach to Numerical Computing
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2014
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Jeff Bezanson
Alan Edelman
Stefan Karpinski
Viral B. Shah
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The Beta-MANOVA Ensemble with General Covariance
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2013
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Alexander Dubbs
Alan Edelman
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The beta-Wishart ensemble
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2013
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Alexander Dubbs
Alan Edelman
Plamen Koev
Praveen S. Venkataramana
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The Beta-MANOVA Ensemble with General Covariance
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2013
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Alexander Dubbs
Alan Edelman
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Random Matrix Theory and Its Innovative Applications
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2012
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Alan Edelman
Yuyang Wang
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PDF
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Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems
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2012
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Jiahao Chen
Eric Hontz
Jeremy M. Moix
Matthew Welborn
Troy Van Voorhis
Alberto Suárez
Ramis Movassagh
Alan Edelman
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Partial freeness of random matrices
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2012
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Jiahao Chen
Troy Van Voorhis
Alan Edelman
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Julia: A Fast Dynamic Language for Technical Computing
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2012
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Jeff Bezanson
Stefan Karpinski
Viral B. Shah
Alan Edelman
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Density of States of Quantum Spin Systems from Isotropic Entanglement
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2011
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Ramis Movassagh
Alan Edelman
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An Efficient Partitioning Oracle for Bounded-Treewidth Graphs
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2011
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Alan Edelman
Avinatan Hassidim
Huy Nguyen
Krzysztof Onak
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An Efficient Partitioning Oracle for Bounded-Treewidth Graphs
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2011
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Alan Edelman
Avinatan Hassidim
Huy Nguyen
Krzysztof Onak
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An Efficient Partitioning Oracle for Bounded-Treewidth Graphs
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2011
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Alan Edelman
Avinatan Hassidim
Huy Nguyen
Krzysztof Onak
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Painlevé Project on the web
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2010
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Folkmar Bornemann
Peter Clarkson
Percy Deift
Alan Edelman
Alexander Its
Daniel W. Lozier
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Isotropic Entanglement
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2010
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Ramis Movassagh
Alan Edelman
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PDF
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Statistical eigen-inference from large Wishart matrices
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2008
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N. Raj Rao
James A. Mingo
Roland Speicher
Alan Edelman
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Sturm Sequences and Random Eigenvalue Distributions
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2008
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James T. Albrecht
Cy Chan
Alan Edelman
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Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples
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2008
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Raj Rao Nadakuditi
Alan Edelman
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The Polynomial Method for Random Matrices
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2007
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N. Raj Rao
Alan Edelman
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PDF
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Sample size cognizant detection of signals in white noise
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2007
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Raj Rao Nadakuditi
Alan Edelman
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PDF
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On the complete pivoting conjecture for a hadamard matrix of order 12
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2007
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Alan Edelman
Walters Mascarenhas
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Sample eigenvalue based detection of high dimensional signals in white noise using relatively few samples
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2007
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N. Raj Rao
Alan Edelman
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From Random Matrices to Stochastic Operators
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2007
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Alan Edelman
Brian Sutton
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PDF
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The Beta-Jacobi Matrix Model, the CS Decomposition, and Generalized Singular Value Problems
|
2007
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Alan Edelman
Brian Sutton
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MOPS: Multivariate orthogonal polynomials (symbolically)
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2007
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Ioana Dumitriu
Alan Edelman
Gene Shuman
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Sample size cognizant detection of signals in white noise
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2007
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N. Raj Rao
Alan Edelman
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Sample eigenvalue based detection of high dimensional signals in white noise using relatively few samples
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2007
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N. Raj Rao
Alan Edelman
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Free Probability, Sample Covariance Matrices, and Signal Processing
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2006
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N. Raj Rao
Alan Edelman
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PDF
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Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models
|
2006
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Ioana Dumitriu
Alan Edelman
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The efficient evaluation of the hypergeometric function of a matrix argument
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2006
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Plamen Koev
Alan Edelman
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Free Probability, Sample Covariance Matrices and Stochastic Eigen-Inference
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2006
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Alan Edelman
N. Raj Rao
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The polynomial method for random matrices
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2006
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N. Raj Rao
Alan Edelman
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PDF
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On the largest principal angle between random subspaces
|
2005
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Pierre-Antoine Absil
Alan Edelman
Plamen Koev
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Advances in random matrix theory
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2005
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Alan Edelman
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PDF
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Eigenvalues of Hermite and Laguerre ensembles: large beta asymptotics
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2005
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Ioana Dumitriu
Alan Edelman
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Random matrix theory
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2005
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Alan Edelman
N. Raj Rao
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+
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Numerical Methods for Eigenvalue Distributions of Random Matrices
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2005
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Alan Edelman
Per‐Olof Persson
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PDF
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Tails of Condition Number Distributions
|
2005
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Alan Edelman
Brian Sutton
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The Efficient Evaluation of the Hypergeometric Function of a Matrix Argument
|
2005
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Plamen Koev
Alan Edelman
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Pascal Matrices
|
2004
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Alan Edelman
Gilbert Strang
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+
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MOPS: Multivariate Orthogonal Polynomials (symbolically)
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2004
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Ioana Dumitriu
Alan Edelman
Gene Shuman
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PDF
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Matrix models for beta ensembles
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2002
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Ioana Dumitriu
Alan Edelman
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+
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Spiral Echo-Planar Trajectories for 3D Non-Fourier Encoded MRI
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2002
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Dimitris Mitsouras
Lawrence P. Panych
Alan Edelman
Gary P. Zientara
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Staircase Failures Explained by Orthogonal Versal Forms
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2000
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Alan Edelman
Yanyuan Ma
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9. Nonlinear Eigenvalue Problems
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2000
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Zhanbing Bai
Gérard L. G. Sleijpen
Henk van der Vorst
Ross A. Lippert
Alan Edelman
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A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm
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1999
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Alan Edelman
Erik Elmroth
Bo Kågström
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The Geometry of Algorithms with Orthogonality Constraints
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1998
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Alan Edelman
T. A. Arias
Steven T. Smith
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A counterexample to a hadamard matrix pivot conjecture
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1998
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Alan Edelman
David Friendman
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PDF
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Multiscale Computation with Interpolating Wavelets
|
1998
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Ross A. Lippert
T. A. Arias
Alan Edelman
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Nonlinear eigenvalue problems
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1998
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Ross A. Lippert
Alan Edelman
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PDF
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The Geometry of Algorithms with Orthogonality Constraints
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1998
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Alan Edelman
T. A. Arias
Steven T. Smith
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The Geometry of Algorithms with Orthogonality Constraints
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1998
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Alan Edelman
T. A. Arias
Steven T. Smith
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A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
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1997
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Alan Edelman
Erik Elmroth
Bo Kågström
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The Probability that a Random Real Gaussian Matrix haskReal Eigenvalues, Related Distributions, and the Circular Law
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1997
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Alan Edelman
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On conjugate gradient-like methods for eigen-like problems
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1996
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Alan Edelman
Steven T. Smith
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Chat
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Erratum to “How many zeros of a random polynomial are real?”
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1996
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Alan Edelman
Eric Kostlan
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Scalable Parallel Numerical Methods and Software Tools for Material Design.
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1995
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Eric J. Bylaska
Scott R. Kohn
Scott B. Baden
Alan Edelman
Ryoichi Kawai
Midori Ong
John H. Weare
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The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms
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1995
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James Demmel
Alan Edelman
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On the Determinant of a Uniformly Distributed Complex Matrix
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1995
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Alan Edelman
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On Parlett's matrix norm inequality for the Cholesky decomposition
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1995
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Alan Edelman
Walter F. Mascarenhas
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PDF
Chat
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Polynomial Roots from Companion Matrix Eigenvalues
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1995
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Alan Edelman
Hironori Murakami
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PDF
Chat
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On the complete pivoting conjecture for a hadamard matrix of order 12
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1995
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Alan Edelman
Walters Mascarenhas
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PDF
Chat
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How many zeros of a random polynomial are real?
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1995
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Alan Edelman
Eric Kostlan
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How many zeros of a random polynomial are real
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1995
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Alan Edelman
Eric Kostlan
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PDF
Chat
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Polynomial roots from companion matrix eigenvalues
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1995
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Alan Edelman
Hironori Murakami
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How many zeros of a random polynomial are real?
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1995
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Alan Edelman
Eric Kostlan
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PDF
Chat
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How many eigenvalues of a random matrix are real?
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1994
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Alan Edelman
Eric Kostlan
Michael Shub
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Scalable Parallel Numerical Methods and Software Tools for Material Design
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1994
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Eric J. Bylaska
S. Khon
Scott B. Baden
Alan Edelman
Ryoichi Kawai
Midori Ong
J.H. Weare
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PDF
Chat
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How Many Eigenvalues of a Random Matrix are Real?
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1994
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Alan Edelman
Eric Kostlan
Michael Shub
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Eigenvalue Roulette and Random Test Matrices
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1993
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Alan Edelman
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PDF
Chat
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On the distribution of a scaled condition number
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1992
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Alan Edelman
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PDF
Chat
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On the Distribution of a Scaled Condition Number
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1992
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Alan Edelman
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The distribution and moments of the smallest eigenvalue of a random matrix of wishart type
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1991
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Alan Edelman
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Snapshots of Mobile Jacobi
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1991
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Alan Edelman
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PDF
Chat
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Eigenvalues and Condition Numbers of Random Matrices
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1988
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Alan Edelman
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Orthogonal polynomials in monotone and convex interpolation
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1988
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Alan Edelman
Charles A. Micchelli
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Admissible slopes for monotone and convex interpolation
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1987
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Alan Edelman
Charles A. Micchelli
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