User profiles for Alan Edelman
Alan EdelmanProfessor of Applied Mathematics, Member Computer Science AI LABS, MIT Verified email at mit.edu Cited by 24172 |
Eigenvalues and condition numbers of random matrices
A Edelman - SIAM journal on matrix analysis and applications, 1988 - SIAM
Given a random matrix, what condition number should be expected? This paper presents a
proof that for real or complex $n \times n$ matrices with elements from a standard normal …
proof that for real or complex $n \times n$ matrices with elements from a standard normal …
The geometry of algorithms with orthogonality constraints
In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann
and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as …
and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as …
Universal differential equations for scientific machine learning
In the context of science, the well-known adage "a picture is worth a thousand words" might
well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML …
well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML …
Random matrix theory
… about the condition numbers of such random matrices as n → ∞ from Edelman (1989). …
Results on the condition number have been extended recently by Edelman and Sutton (2004), …
Results on the condition number have been extended recently by Edelman and Sutton (2004), …
The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms
The set of n by n matrices with a given Jordan canonical form defines a subset of matrices in
complex n 2 dimensional space. We analyze one classical approach and one new …
complex n 2 dimensional space. We analyze one classical approach and one new …
The probability that a random real gaussian matrix haskreal eigenvalues, related distributions, and the circular law
A Edelman - journal of multivariate analysis, 1997 - Elsevier
LetAbe annbynmatrix whose elements are independent random variables with standard
normal distributions. Girko's (more general) circular law states that the distribution of …
normal distributions. Girko's (more general) circular law states that the distribution of …
Julia: A fresh approach to numerical computing
Bridging cultures that have often been distant, Julia combines expertise from the diverse
fields of computer science and computational science to create a new approach to numerical …
fields of computer science and computational science to create a new approach to numerical …
Julia: A fast dynamic language for technical computing
Dynamic languages have become popular for scientific computing. They are generally
considered highly productive, but lacking in performance. This paper presents Julia, a new …
considered highly productive, but lacking in performance. This paper presents Julia, a new …
How many zeros of a random polynomial are real?
A Edelman, E Kostlan - Bulletin of the American Mathematical Society, 1995 - ams.org
We provide an elementary geometric derivation of the Kac integral formula for the expected
number of real zeros of a random polynomial with independent standard normally distributed …
number of real zeros of a random polynomial with independent standard normally distributed …
Matrix models for beta ensembles
I Dumitriu, A Edelman - arXiv preprint math-ph/0206043, 2002 - arxiv.org
This paper constructs tridiagonal random matrix models for general ($\beta>0$) $\beta$-Hermite
(Gaussian) and $\beta$-Laguerre (Wishart) ensembles. These generalize the well-…
(Gaussian) and $\beta$-Laguerre (Wishart) ensembles. These generalize the well-…