Publications

**Contents:**

SCIENTIFIC COMPUTING

PARALLEL COMPUTING

RANDOM EIGENVALUES etc.

NUMERICAL LINEAR ALGEBRA

APPROXIMATION THEORY

THESIS

When is x*(1/x) not equal to 1? , by A Edelman (never published except for the web -- just for fun) (1994).

The Mathematics of the Pentium Division Bug , by A Edelman SIAM Review 39, (1997), 54-67.

A Physically Based Numerical Color Calibration Algorithm for Film , by A Edelman, Frank Wang, and Arun Rao (2003).

An Efficient Paritioning Oracle for Bounded-Treewidth Graphs , by A Edelman, A. Hassidim, Huy Nguyen, K. Onak Proceedings. Lecture Notes in Computer Science 6845 Springer (2011) .

Building Blocks and Excluded Sums , by Erik Demaine, Martin Demaine, Alan Edelman, Charles Leiserson, Per-Olof Persson SIAM News, v. 28, number 1, page 1,4,6 (2005) .

Fast Magnetic Resonance Imaging via Adaptive Broadband Encoding of the MR Signal Content , by Dimitris Mitsouras, Frank Rybicki, A Edelman, Gary Zientara. IEEE Transactions on Medical Imaging (2004).

Non-Fourier Encoded Parallel MRI Using Multiple Receiver Coils , by Mitsouras D., Hoge W.S., Rybicki F.J., Kyriakos W., Edelman A., Zientara G.P. Magnetic Resonance in Medicine. (2004).

Multiscale Computation with Interpolating Wavelets, by Ross Lippert, T. Arias, and A. Edelman. Journal of Computational Physics 140,pp.278-310, (1998).

A Fast Projected Conjugate Gradient Algorithm for Training Support Vector Machines , by T. Wen and A. Edelman. in Fast Algorithms for Structured Matrices; Theory and Applications, edited by Vadim Olshevsky, Contemporary Mathematics 323, (2003).

The geometry of algorithms with orthogonality constraints, by T.Arias, A.Edelman, and S. Smith.
SIAM J Matrix Analy Appl 20 (1998), 303-353.

Curvature
in Conjugate Gradient Eigenvalue Computation with Applications to Materials
and Chemistry Calculations, by T.Arias, A.Edelman, and S.Smith. Proceedings
of the 1994 SIAM Applied Linear Algebra Conference J.G. Lewis, ed., SIAM, Philadelphia,
(1994), 233-238.

Nonlinear eigenvalue problems with orthogonality constraints by R. Lippert and A. Edelman as Chapter 8.3 in Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM. Also code is available.

Reflections on the Large Scale Matrix Computations in Lattice QCD Conference by R. Brower, J. Demmel, A Edelman, G. Hockney (1995 never published). This is a little note whipped up after a very nice conference held in Lexington Kentucky

Julia: A Fast Dynamic Language for Technical Computing
, by Jeff Bezanson, Stefan Karpinski, Viral Shah, and A. Edelman,
http://arxiv.org/pdf/1209.5145v1.pdf

Parallel MATLAB: doing it right, by A. Edelman,
R. Choy, Proceedings of the IEEE volume 93, issue 2, Feb 2005 pp 331-341.

Petabricks: A Language and Compiler for Algorithmic
Choice., by
Jason Ansel, Yee Lok Wong, Marek Olszewski, Qin Zhao, Alan Edelman,
Saman Amarasinghe.
ACM SIGPLAN Conference on Programming Language Design and Implementation.
Dublin, Ireland. Jun, 2009.

Language and Compiler Support for Auto-Tuning Variable-Accuracy Algorithms.
, by
Jason Ansel, Yee Lok Won ans Cy Chan, Marek Olszewski, Alan Edelman, Saman
Amarasinghe.
The International Symposium on Code Generation and Optimization.
Chamonix, France. Apr, 2011

Autotuning Multigrid with PetaBricks.
, by
Cy Chan, Jason Ansel, Yee Lok Wong, Saman Amarasinghe, Alan Edelman.
ACM/IEEE Conference on Supercomputing.
Portland, OR. Nov, 2009

The Future Fast Fourier Transform?, by A. Edelman,
P. McCorquodale, and S. Toledo. SIAM Journal on Scientific Computing.
SIAM J Scientific Computing 20 1094-1114 (1998)

Index Transformation Algorithms in a Linear Algebra Framework, by A. Edelman, S. Heller and S. L. Johnsson. IEEE Transactions on Parallel and Distributed Systems 5 (1994), 1302--1309.)

Large Numerical Linear Algebra in 1994: The Continuing Influence of Parallel Computing, by A. Edelman. Proceedings of the 1994 Scalable High Performance Computing Conference. IEEE Computer Society Press, Los Alamitos, CA, (1994), 781--787.

Hypercube algorithms for direct N-body solvers for different granularities, by A. Edelman, J. Brunet, and J. Mesirov. SIAM Journal on Scientific Computing. 14 (1993), 1143--1158.

Large Dense Numerical Linear Algebra in 1993: The Parallel Computing Influence, by A. Edelman. Journal of Supercomputing Applications. 7 (1993), 113--128.

Matrix multiplication on hypercubes using full bandwidth and constant storage, by C.T.Ho, S.L.Johnsson , and A. Edelman. The Sixth Distributed Memory Computing Conference Proceedings IEEE Computer Society Press (1991), 447--451.

Optimal matrix transposition and bit reversal on hypercubes: All--to--all personalized communication, by A. Edelman. J. Parallel Dist. Comp. 11 (1991), 328--331.

The first annual large dense linear system survey, by A. Edelman. The SIGNUM Newsletter 26 (October 1991), 6--12.

Guess what? We have a hypercube, by A. Edelman. Thinking Machines Corporation Semi-Internal Report, (1989) - not published.

The beta-Wishart ensemble . by Alexander Dubbs, Alan Edelman, Plamen Koev, and Praveen Venkataramana Journal of Mathematical Physics 54, 083507 (2013).

Computing with Beta Ensembles and Hypergeometric Functions . by Vesselin Drensky, Alan Edelman, Tierney Genoar, Raymond Kan, and Plamen Koev RMTA (2014).

The Beta-MANOVA Ensemble with General Covariance . by Alexander Dubbs and Alan Edelman

Eigenvalue distributions of Beta-Wishart matrices by Alan Edelman and Plamen Koev RMTA (2013).

Random Triangle Theory with Geometry and Applications . To appear FOCM (2013).

Random Matrix Theory, Numerical Computation and Applications . (2013).

Isotropic Entanglement, by Ramis Movassagh and Alan Edelman . (2013).

Density of States of Quantum Spin Systems from Isotropic Entanglement , by Ramis Movassagh and Alan Edelman . Phys. Rev. Lett. 107, 097205 (2011).

Condition Numbers of Indefinite Rank 2 Ghost Wishart Matrices by Ramis Movassagh and Alan Edelman . (2012).

Sample Size Cognizant Detection of Signals in White Noise by Raj Rao Nadakuti and Alan Edelman . (2007).

Partial Freeness of Random Matrices by Jiahao Chen and Alan Edelman . (2012).

The Random Matrix Technique of Ghosts and Shadows . Markov Processes and Related Fields (2011).

The Polynomial Method for Random Matrices by N. Raj Rao and A. Edelman Foundations of Computational Mathematics (2008)

On Computing Schur Functions and Series Thereof by Cy Chan, Vesselin Drensky, Raymond Kan, Plamen Koev and A. Edelman Journal of Algebraic Combinatorics (submitted)

Sturm Sequences and Random Eigenvalue distributions by James Albrecht, Cy Chan, and A. Edelman Foundations of Computational Mathematics (accepted)

On the Probability Distribution of the Outputs of the Diagonally Loaded Capon-MVDR Processor by N. Raj Rao and A. Edelman Signals, Systems and Computers, 2005. Conference Record of the Thirty-Ninth Asilomar Conference on Publication Date: October 28 - November 1, 2005 pages: 1717- 1723.

From Random Matrices to Stochastic Operators by Brian Sutton and A. Edelman Journal of Statistical Physics 127 (2007), no. 6, 1121-1165.

Statistical eigen-inference from large Wishart Matrices by N Raj Rao, James Mingo, Roland Speicher and A. Edelman Annals of Statistics (2008)

Sample eigenvalue based detection of high-dimensional signals in white noise using relatively few samples by N Raj Rao and A. Edelman IEEE Transactions of Signal Processing (2008)

The beta-Jacobi matrix model, the CS decomposition, and generalized singular value problems by Brian Sutton and A. Edelman 8, (2008), no 2. Foundations of Computational Mathematics.

Global Spectrum Fluctuations for the beta-Hermite and beta-Laguerre ensembles via matrix models, by Ioana Dumitriu and A. Edelman Journal of Mathematical Physics 47 (2006).

On the Efficient Evaluation of the Hypergeometric Function of a Matrix Argument , by Plamen Koev and A. Edelman Mathematics of Computation. (2006).

Tails of Condition Number Distributions , by Brian Sutton and A. Edelman SIMAX (2005), no. 2, 547-560.

A linear-time algorithm for evaluating series of Schur functions , by Cy Chan, Vesselin Drensky, Alan Edelman, and Plamen Koev. Preprint.

On the Largest Principal Angle between Random Subspaces , by P.A. Absil, Plamen Koev and A. Edelman. LAA (2006).

Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics , by Ioana Dumitriu and A. Edelman. Annales de l'Institut Henri Poincare (B), 41 (6) (2005), 1083-1099.

Matrix Models for Beta Ensembles, by Ioana Dumitriu and A. Edelman. Journal of Mathematical Physics 43, (2002), 5830--5847.

The Probability
that a Random Real Gaussian Matrix Has k Real Eigenvalues, Related Distributions,
and the Circular Law, by A. Edelman, Journal of Multivariate Analysis 60,
(1997), 203--232.

How many zeros of a random polynomial are real?,
by A. Edelman and E. Kostlan Bulletin of the American Mathematical Society 32
(1995), 1--37.

On the determinant of a uniformly distributed complex matrix, by A. Edelman. Journal of Complexity 11 (1995), 352--357.

How many eigenvalues of a random matrix are real?, by A. Edelman, E. Kostlan, and M. Shub. J. Amer. Math. Soc. 7 (1994), 247--267.

The road from Kac's matrix to Kac's random polynomials, by A.Edelman and E.Kostlan. Proceedings of the 1994 SIAM Applied Linear Algebra Conference J.G. Lewis, ed., SIAM, Philadelphia (1994), 503--507.

Eigenvalue Roulette and Random Test Matrices, by A. Edelman. Linear Algebra for Large Scale and Real-Time Applications edited by Marc S. Moonen, Gene H. Golub, and Bart L. R. De Moor. NATO ASI Series (1992), 365--368.

On the distribution of a scaled condition number, by A. Edelman. Mathematics of Computation 58 (1992), 185--190.

The distribution and moments of the smallest eigenvalue of a random matrix of Wishart type, by A. Edelman. Lin. Alg. Appl. 159 (1991), 55-80.

Eigenvalues and condition numbers of random matrices, by A. Edelman. SIAM Journal on Matrix Analysis and Applications 9 (1988), 543--560.

Pascal Matrices by G. Strang and A. Edelman. American Mathematical Monthly, March 1004.

Staircase failures explained by orthogonal versal
forms, by A. Edelman and Y. Ma. SIAM J Matrix Analy Appl 21 (2000), 1004-1025.

A Counterexample
to a Hadamard Matrix Pivot Conjecture, by A. Edelman and D. Friedman. J
of Linear and Multilinear Algebra (1998), 44, 53--56.

Non-generic eigenvalue perturbations of Jordan blocks, by A. Edelman and Y. Ma. Linear Algebra and Applications 273, (1998), 45--63.

The Computation and Sensitivity of Double Eigenvalues, by A. Edelman and Ross Lippert. Advances in Computational Mathematics 202 of Lecture Notes in Pure and Applied Mathematics, (1998).

A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformation, by A. Edelman, E. Elmroth, and B. Kågström. (1995)

A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification Enhanced Staircase Algorithm , by A. Edelman, E. Elmroth, and B. Kågström SIAM J Matrix Anal Applications 20, (1999), 667--699.

A simple estimate of the condition number of a linear system, by H.W. Guggenheimer, A. Edelman, and C.R. Johnson. College Mathematics Journal,(1995), 2--5.

On Parlett's matrix norm inequality for the Cholesky decomposition, by A. Edelman and W. Mascarenhas Numerical Linear Algebra with Applications. 2 (1995), 243--250.

On the complete pivoting conjecture for a Hadamard matrix of order 12, by A. Edelman and W. Mascarenhas. J of Linear and Multilinear Algebra 38 (1995), 181--187.

Polynomial roots from companion matrix eigenvalues, by A. Edelman and H. Murakami, Mathematics of Computation. 64 (1995), 763--776.

The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms, by J. Demmel and A. Edelman. Linear Algebra and its Applications 230 (1995), 61--87.

Scaling for orthogonality, by A. Edelman and G.W. Stewart. Transactions on Signal Processing 41 (1993), 1676--1677.

The complete pivoting conjecture for Gaussian Elimination is false, by A Edelman. The Mathematica Journal 2 (1992), 58--61.

Snapshots
of Mobile Jacobi, by A. Edelman. Numerical Linear Algebra, Digital Signal
Processing and Parallel Algorithms, NATO ASI Series F. 70 Springer-Verlag (1991),
485--488. (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!)

**APPROXIMATION THEORY**

Positivity, monotonicity, or convexity-preserving
cubic and quintic Hermite interpolation, by R. Dougherty, A. Edelman, and J.M.Hyman.
Mathematics of Computation (1989), 471--494.

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

On locally supported basis functions for the representation of geometrically continuous curves, by N. Dyn, A. Edelman and C. Micchelli Analysis 7 (1987), 313--341.

**THESIS**

Eigenvalues
and Condition Numbers of Random Matrices, by A. Edelman
MIT PhD Dissertation, 1989. (As of 2002, the figures are now included in this
file. They were all recomputed!)

We would like to thank NSF for all of their support for award grants 9971591, 9709607, 9501278, 9404326, 8953828, 0314286, 0411962 .