ALAN EDELMAN

This is not complete, but whose web page is?

One way to think about the subtleties of the IEEE standard is to consider when x*(1/x)=1. This is a surprisingly good problem. (I have never published this work other than this open dissemination on the WEB.)

I just found out that my Patent can be found on the web. US5367692

One of my favorite works is a joint paper with Eric Kostlan on How many roots of a random polynomial are real? It appears in the January 1995 Bulletin and we are excited to learn that this paper is the winner of the 1998 Chauvenet Prize.

People often confuse nonlinear conjugate gradient with linear conjugate gradient for the eigenproblem. The latter seems related to Lanczos just to further the confusion. We sort this out in the paper On Conjugate Gradient-Like Methods for Eigen-Like Problems with Steve Smith.

SCIENTIFIC COMPUTING

* The geometry of algorithms with orthogonality constraints by T.Arias, A.Edelman, and S. Smith.

* 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.

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

PARALLEL COMPUTING

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

* 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.

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

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

* 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..)

* 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.

* 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.

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

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

RANDOM EIGENVALUES etc.

* 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.

* 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.

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

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

* 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.

* 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.

NUMERICAL LINEAR ALGEBRA

* The Computation and Sensitivity of Double Eigenvalues .

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

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

* 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 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.

* A Counterexample to a Hadamard Matrix Pivot Conjecture by A. Edelman and D. Friedman. J of Linear and Multilinear Algebra (1998), to appear.

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

* A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: Stratifications, by A. Edelman, E. Elmroth, and B. Kågström.

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

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

* 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.

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

* 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.

* 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

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

* 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.

* 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 postscript file. They were all recomputed!)