Alan Edelman

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Scientific Computing

Robust benchmarking in noisy environments.
Chen, J., Edelman, A., & Revels, J. (2016).
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Abstract
An Efficient Partitioning Oracle for Bounded-Treewidth Graphs
Edelman, A., Hassidim, A., Nguyen, H.N., & Onak, K. (2011). In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (pp. 530-541). Springer Berlin Heidelberg.
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arXiv
Abstract
Enhancing the acquisition efficiency of fast magnetic resonance imaging via broadband encoding of signal content
Mitsouras, D., Zientara, G. P., Edelman, A., & Rybicki, F. J. (2006). Magnetic resonance imaging, 24(9), 1209-1227.
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Abstract
Building Blocks and Excluded Sums
Demaine, E. D., Demaine, M. L., Edelman, A., Leiserson, C. E., & Persson, P. O. (2005). SIAM News, 38(1), 1-5.
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Non-Fourier Encoded Parallel MRI Using Multiple Receiver Coils
Mitsouras, D., Hoge, W. S., Rybicki, F. J., Kyriakos, W. E., Edelman, A., & Zientara, G. P. (2004). Magnetic resonance in medicine, 52(2), 321-328.
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Abstract
Fast Multipole: It's all about Adding Functions in Finite Precision
Edelman, A., & Persson, P. 0. (2004, never published).
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A Physically Based Numerical Color Calibration Algorithm for Film
Edelman, A., Wang, F., & Rao, A. (2003)
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A Fast Projected Conjugate Gradient Algorithm for Training Support Vector Machines
Wen, T., Edelman, A., & Gorsich, D. (2001, August). In Contemporary mathematics (pp. 245-263). American Mathematical Society.
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Abstract
Nonlinear eigenvalue problems with orthogonality constraints
Edelman, A., & Lippert, R. (2000). (section 8.3). Bai, Z., Demmel, J., Dongarra, J., Ruhe, A. and Vorst, H. van der, editors: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. Philidelphia: SIAM.
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The geometry of algorithms with orthogonality constraints
Edelman, A., Arias, T. A., & Smith, S. T. (1998). SIAM journal on Matrix Analysis and Applications, 20(2), 303-353.
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arXiv
Abstract
Multiscale Computation with Interpolating Wavelets
Lippert, R. A., Arias, T. A., & Edelman, A. (1998). Journal of Computational Physics, 140(2), 278-310.
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arXiv
Abstract
The Mathematics of the Pentium Division Bug
Edelman, A. (1997). SIAM Review, 39(1), 54-67.
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On Conjugate Gradient-Like Methods for Eigen-Like Problems
Edelman, A., & Smith, S. T. (1996). BIT Numerical Mathematics, 36(3), 494-508.
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Abstract
Reflections on the Large Scale Matrix Computations in Lattice QCD Conference
Brower, R., Demmel, J., Edelman, A., & Hockney, G. (1995, never published). This is a little note whipped up after a very nice conference held in Lexington Kentucky
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Curvature in Conjugate Gradient Eigenvalue Computation with Applications to Materials and Chemistry Calculations
Edelman, A., Arias, T. A., & Smith, S. T. (1994). In In Proceedings of the 1994 SIAM Applied Linear Algebra Conference.
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Abstract
When is x*(1/x) not equal to 1?
Edelman, A. (1994). Never published except for the web -- just for fun.
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Random Eigenvalues etc.

Beyond Universality in Random Matrix Theory
Edelman, A., Guionnet, A., & Péché, S. (2016). The Annals of Applied Probability, 26(3), 1659-1697.
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arXiv
Abstract
Infinite random matrix theory, tridiagonal bordered Toeplitz matrices, and the moment problem
Dubbs, A., & Edelman, A. (2015). Linear Algebra and its Applications, 467, 188-201.
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Abstract
The singular values of the GUE (less is more)
Edelman, A., & La Croix, M. (2015, October). Random Matrices:Theory and Applications, 4(4), Issue 04.
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arXiv
Abstract
Random Matrix Theory, Numerical Computation and Applications
Edelman, A., Sutton, B. D., & Wang, Y. (2014). Modern Aspects of Random Matrix Theory, 72, 53.
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The Beta-MANOVA Ensemble with General Covariance
Dubbs, A., & Edelman, A. (2014). Random Matrices: Theory and Applications, 3(01), 1450002.
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arXiv
Abstract
Low-temperature random matrix theory at the soft edge
Edelman, A., Persson, P. O., & Sutton, B. D. (2014). Journal of Mathematical Physics, 55(6), 063302.
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Abstract
Computing with Beta Ensembles and Hypergeometric Functions
Drensky, V., Edelman, A., Genoar, K., Kan, R., & Koev, P. (2014). RMTA.
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Eigenvalue distributions of Beta-Wishart matrices
Edelman, A., & Koev, P. (2014). Random Matrices: Theory and Applications, 3(02), 1450009.
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Abstract
Random Matrix Theory and its Innovative Applications
Edelman, A., & Wang, Y. (2013). In Advances in Applied Mathematics, Modeling, and Computational Science (pp. 91-116). Springer US.
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Abstract
The beta-Wishart ensemble
Dubbs, A., Edelman, A., Koev, P., & Venkataramana, P. (2013). Journal of Mathematical Physics, 54(8), 083507.
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arXiv
Abstract
Isotropic Entanglement
Edelman, A., & Movassagh, R. (2010, revised 2012). Isotropic entanglement. arXiv preprint arXiv:1012.5039.
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arXiv
Abstract
Error Analysis of Free Probability Approximations to the Density of States of Disordered Systems
Chen, J., Hontz, E., Moix, J., Welborn, M., Van Voorhis, T., Suárez, A., ... & Edelman, A. (2012). Physical review letters, 109(3), 036403.
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arXiv
Abstract
Condition Numbers of Indefinite Rank 2 Ghost Wishart Matrices
Edelman, A., & Movassagh, R. (2015, October). Linear Algebra and its Applications, 483, 342-351.
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arXiv
Abstract
Random Triangle Theory with Geometry and Applications
Edelman, A., & Strang, G. (2012). Foundations of Computational Mathematics, 15(3), 681-713.

Accompanying Julia Notebook [html] [ipynb]

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Abstract
Partial Freeness of Random Matrices
Chen, J., Van Voorhis, T., & Edelman, A. (2012). arXiv preprint arXiv:1204.2257.
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arXiv
Abstract
Density of States of Quantum Spin Systems from Isotropic Entanglement
Edelman, A., & Movassagh, R. (2011). Physical review letters, 107(9), 097205.
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arXiv
Abstract
The Random Matrix Technique of Ghosts and Shadows
Edelman, A. (2010). Markov Processes and Related Fields, 16(4), 783-790.
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Sturm Sequences and Random Eigenvalue distributions
Albrecht, J. T., Chan, C. P., & Edelman, A. (2009). Foundations of Computational Mathematics, 9(4), 461-483.
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Abstract
Statistical eigen-inference from large Wishart Matrices
Rao, N. R., Mingo, J. A., Speicher, R., & Edelman, A. (2008). The Annals of Statistics, 2850-2885.
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arXiv
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The Polynomial Method for Random Matrices
Rao, N. R., & Edelman, A. (2008). Foundations of Computational Mathematics, 8(6), 649-702.
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arXiv
Abstract
On Computing Schur Functions and Series Thereof
Chan, C., Drensky, V., Edelman, A., Kan, R., & Koev, P. (2008). preprint.
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The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems
Edelman, A., & Sutton, B. D. (2008). Foundations of Computational Mathematics, 8(2), 259-285.
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Sample eigenvalue based detection of high-dimensional signals in white noise using relatively few samples
Nadakuditi, R. R., & Edelman, A. (2008). Signal Processing, IEEE Transactions on, 56(7), 2625-2638.
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arXiv
Abstract
Sample Size Cognizant Detection of Signals in White Noise
Nadakuditi, R. R., & Edelman, A. (2007, June). In Signal Processing Advances in Wireless Communications, 2007. SPAWC 2007. IEEE 8th Workshop on (pp. 1-5). IEEE.
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arXiv
Abstract
From Random Matrices to Stochastic Operators
Edelman, A., & Sutton, B. D. (2007). Journal of Statistical Physics, 127(6), 1121-1165.
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arXiv
Abstract
MOPS: Multivariate Orthogonal Polynomials (symbolically)
Dumitriu, I., Edelman, A., & Shuman, G. (2007). Journal of symbolic computation, 42(6), 587-620.
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arXiv
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On the Largest Principal Angle between Random Subspaces
Absil, P. A., Edelman, A., & Koev, P. (2006). Linear Algebra and its applications, 414(1), 288-294.
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Abstract
Global Spectrum Fluctuations for the beta-Hermite and beta-Laguerre ensembles via matrix models
Dumitriu, I., & Edelman, A. (2006). Journal of Mathematical Physics, 47(6), 063302.
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arXiv
Abstract
On the Efficient Evaluation of the Hypergeometric Function of a Matrix Argument
Koev, P., & Edelman, A. (2006). Mathematics of Computation, 75(254), 833-846.
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arXiv
Abstract
On the Probability Distribution of the Outputs of the Diagonally Loaded Capon-MVDR Processor
Nadakuditi, R. R., & Edelman, A. (2005, October). In Signals, Systems and Computers, 2005. Conference Record of the Thirty-Ninth Asilomar Conference on (pp. 1717-1723). IEEE.

Numerical Methods for Eigenvalue Distributions of Random Matrices
Edelman, A., & Persson, P. O. (2005). arXiv preprint math-ph/0501068.
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arXiv
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Tails of Condition Number Distributions
Edelman, A., & Sutton, B. D. (2005). SIAM journal on matrix analysis and applications, 27(2), 547-560.
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Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics
Dumitriu, I., & Edelman, A. (2005). In Annales de l'IHP Probabilités et statistiques, 41(6), 1083-1099.
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arXiv
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Matrix Models for Beta Ensembles
Dumitriu, I., & Edelman E. (2002). Journal of Mathematical Physics, 43, 5830--5847.
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arXiv
Abstract
How many zeros of a random polynomial are real?
Edelman, A., & Kostlan, E. (1995). Bulletin of the American Mathematical Society, 32(1), 1-37.
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arXiv
Abstract
On the determinant of a uniformly distributed complex matrix
Edelman, A. (1995). Journal of Complexity, 11(3), 352-357.
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How many eigenvalues of a random matrix are real?
Edelman, A., Kostlan, E., & Shub, M. (1994). Journal of the American Mathematical Society, 7(1), 247-267.
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Abstract
The road from Kac's matrix to Kac's random polynomials
Edelman, A. & Kostlan, E. (1994). Proceedings of the 1994 SIAM Applied Linear Algebra Conference J.G. Lewis, ed., SIAM, Philadelphia, 503--507
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Eigenvalue Roulette and Random Test Matrices
Edelman, A. (1993). In Linear Algebra for Large Scale and Real-Time Applications (pp. 365-368). Springer Netherlands.
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The Circular Law and the Probability that a Random Matrix Has $k$ Real Eigenvalues
Edelman, A. (1993). preprint.
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On the distribution of a scaled condition number
Edelman, A. (1992). Mathematics of Computation, 58(197), 185-190.
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The distribution and moments of the smallest eigenvalue of a random matrix of Wishart type
Edelman, A. (1991). Linear algebra and its applications, 159, 55-80.

Abstract
Eigenvalues and Condition Numbers of Random Matrices
Edelman, A. (1989). MIT PhD Dissertation(4).

(As of 2002, the figures are now included in this file. They were all recomputed!)

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Eigenvalues and condition numbers of random matrices
Edelman, A. (1988). SIAM Journal on Matrix Analysis and Applications, 9(4), 543-560.
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A linear-time algorithm for evaluating series of Schur functions
Chan, C., Drensky, V., Edelman, A., & Koev, P. preprint
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Parallel Computing

Array Operators Using Multiple Dispatch: A design methodology for array implementations in dynamic languages
Bezanson, J., Chen, J., Karpinski, S., Shah, V., & Edelman, A. (2014, June). In Proceedings of ACM SIGPLAN International Workshop on Libraries, Languages, and Compilers for Array Programming (p. 56). ACM.
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Parallel Prefix Polymorphism Permits Parallelization, Presentation & Proof
Chen, J., & Edelman, A. (2014, November). In Proceedings of the 1st First Workshop for High Performance Technical Computing in Dynamic Languages (pp. 47-56). IEEE Press.
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Abstract
Julia: A Fast Dynamic Language for Technical Computing
Bezanson, J., Karpinski, S., Shah, V. B., & Edelman, A. (2012). arXiv preprint arXiv:1209.5145.
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arXiv
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Language and Compiler Support for Auto-Tuning Variable-Accuracy Algorithms
Ansel, J., Wong, Y. L., Chan, C., Olszewski, M., Edelman, A., & Amarasinghe, S. (2011, April). In Proceedings of the 9th Annual IEEE/ACM International Symposium on Code Generation and Optimization (pp. 85-96). IEEE Computer Society.
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Autotuning Multigrid with PetaBricks
Chan, C., Ansel, J., Wong, Y. L., Amarasinghe, S., & Edelman, A. (2009, November). In High Performance Computing Networking, Storage and Analysis, Proceedings of the Conference on (pp. 1-12). IEEE.
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Petabricks: A Language and Compiler for Algorithmic Choice
Ansel, J., Chan, C., Wong, Y. L., Olszewski, M., Zhao, Q., Edelman, A., & Amarasinghe, S. (2009). (Vol. 44, No. 6, pp. 38-49). ACM.
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Star-P User Guide
(2006). Interactive Supercomputing.
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Getting Started with Star-P: Taking Your First Test-Drive
(2006). Interactive Supercomputing
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Parallel MATLAB: doing it right
Choy, R., & Edelman, A. (2005). Proceedings of the IEEE, 93(2), 331-341.
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Star-P: High productivity parallel computing
Choy, R., Edleman, A., Gilbert, J. R., Shah, V., & Cheng, D. (2004). Massachusetts Institute of Technology, Cambridge, MA.
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The Future Fast Fourier Transform?
Edelman, A., McCorquodale, P., & Toledo, S. (1998). SIAM Journal on Scientific Computing, 20(3), 1094-1114.
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Interactive Supercomputing with MITMatlab
Husbands, P., Isbell Jr, C. L., & Edelman, A. (1998).
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Index Transformation Algorithms in a Linear Algebra Framework
Edelman, A., Heller, S., & Johnsson, S. L. (1994). Parallel and Distributed Systems, IEEE Transactions on, 5(12), 1302-1309.
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Large Numerical Linear Algebra in 1994: The Continuing Influence of Parallel Computing
Edelman, A. (1994, May). In Scalable High-Performance Computing Conference, 1994., Proceedings of the (pp. 781-787). IEEE.
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Hypercube algorithms for direct N-body solvers for different granularities
Brunet, J. P., Mesirov, J. P., & Edelman, A. (1993). SIAM Journal on Scientific Computing, 14(5), 1143-1158.

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Large Dense Numerical Linear Algebra in 1993: The Parallel Computing Influence
Edelman, A. (1993). International Journal of High Performance Computing Applications, 7(2), 113-128.
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Optimal matrix transposition and bit reversal on hypercubes: All--to--all personalized communication
Edelman, A. (1991). Journal of Parallel and Distributed Computing<, 11(4), 328-331.
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Matrix multiplication on hypercubes using full bandwidth and constant storage
Ho, C. T., & Johnsson, L. (1991). In Sixth Distributed Memory Computing Conference (pp. 447-451).
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The first annual large dense linear system survey
Edelman, A. (1991). ACM SIGNUM Newsletter, 26(4), 6-12.
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Guess what? We have a hypercube
Edelman, A. (1989, not published )Thinking Machines Corporation Semi-Internal Report.
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Interactive Supercomputing’s Star-P Platform: Parallel MATLAB and MPI Homework Classroom Study on High Level Language Productivity
Edelman, A., Husbands, P., & Leibman, S. (2006). Massachusetts Institute of Technology, Cambridge, MA. (No. DOE/FE/25631-1).
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Numerical Linear Algebra

Pascal Matrices
Edelman, A., & Strang, G. (2004). American Mathematical Monthly, 189-197.
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Staircase failures explained by orthogonal versal forms
Edelman, A., & Ma, Y. (2000). SIAM Journal on Matrix Analysis and Applications, 21(3), 1004-1025.
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A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification Enhanced Staircase Algorithm
Edelman, A., Elmroth, E., & Kågström, B. (1999). SIAM Journal on Matrix Analysis and Applications, 20(3), 667-699.
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The Computation and Sensitivity of Double Eigenvalues
Lippert, R. A., & Edelman, A. (1999). Advances in Computational Mathematics, Lecture Notes in Pure and Appl. Math, 202, 353-393.
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A Counterexample to a Hadamard Matrix Pivot Conjecture
Edelman, A., & Friendman, D. (1998). Linear and Multilinear Algebra, 44(1), 53-56.

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Non-generic eigenvalue perturbations of Jordan blocks
Ma, Y., & Edelman, A. (1998). Linear algebra and its applications, 273(1), 45-63.
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A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformation
Edelman, A., Elmroth, E., & Kågström, B. (1997). SIAM Journal on Matrix Analysis and Applications, 18(3), 653-692.

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Polynomial roots from companion matrix eigenvalues
Edelman, A., & Murakami, H. (1995). Mathematics of Computation, 64(210), 763-776.
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On the complete pivoting conjecture for a Hadamard matrix of order 12
Edelman, A., & Mascarenhas, W. (1995). Linear and Multilinear Algebra, 38(3), 181-187.
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The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms
Demmel, J. W., & Edelman, A. (1995). Linear algebra and its applications, 230, 61-87.
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On Parlett's matrix norm inequality for the Cholesky decomposition
Edelman, A., & Mascarenhas, W. F. (1995). Numerical linear algebra with applications, 2(3), 243-250.
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A simple estimate of the condition number of a linear system
Guggenheimer, H. W., Edelman, A. S., & Johnson, C. R. (1995). College Mathematics Journal, 2-5.

Scaling for orthogonality
Edelman, A., & Stewart, G. W. (1993). Signal Processing, IEEE Transactions on, 41(4), 1676-1677.
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The complete pivoting conjecture for Gaussian Elimination is false
Edelman, A. (1992). Mathematica Journal, 2(2), 58-61.
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Snapshots of Mobile Jacobi
Edelman, A. (1991). In Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms (pp. 485-488). Springer Berlin Heidelberg.

(What a shame that I do not have the pictures available. Even better would be to put the original video on line. Maybe some day!)

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Approximation Theory

Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation
Dougherty, R. L., Edelman, A. S., & Hyman, J. M. (1989). Mathematics of Computation, 52(186), 471-494.

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On locally supported basis functions for the representation of geometrically continuous curves
Dyn, N., Edelman, A., & Micchelli, C. A. (1987). Analysis, 7(3-4), 313-342.

Admissible slopes for monotone and convex interpolation
Edelman, A., & Micchelli, C. A. (1987). Numerische Mathematik, 51(4), 441-458.
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