150 citations · 367 across the 12 of their papers we have counts for
12 papers
Structured Divide-and-Conquer for the Definite Generalized Eigenvalue Problem
James Demmel, Ioana Dumitriu, Ryan Schneider
This paper presents a fast, randomized divide-and-conquer algorithm for the definite generalized eigenvalue problem, which corresponds to pencils in which and are H…
Fast and Inverse-Free Algorithms for Deflating Subspaces
James Demmel, Ioana Dumitriu, Ryan Schneider
This paper explores a key question in numerical linear algebra: how can we compute projectors onto the deflating subspaces of a regular matrix pencil , in particular without…
Generalized Pseudospectral Shattering and Inverse-Free Matrix Pencil Diagonalization
James Demmel, Ioana Dumitriu, Ryan Schneider
We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any matrix pencil . The bulk of the algorithm rests on a randomi…
Randomized Numerical Linear Algebra : A Perspective on the Field With an Eye to Software
Riley Murray, James Demmel, Michael W. Mahoney +10
Randomized numerical linear algebra - RandNLA, for short - concerns the use of randomization as a resource to develop improved algorithms for large-scale linear algebra computation…
Fast Exact Leverage Score Sampling from Khatri-Rao Products with Applications to Tensor Decomposition
Vivek Bharadwaj, Osman Asif Malik, Riley Murray +3
We present a data structure to randomly sample rows from the Khatri-Rao product of several matrices according to the exact distribution of its leverage scores. Our proposed sampler…
A Generalized Randomized Rank-Revealing Factorization
Grey Ballard, James Demmel, Ioana Dumitriu +1
We introduce a Generalized Randomized QR-decomposition that may be applied to arbitrary products of matrices and their inverses, without needing to explicitly compute the products…
Communication-optimal parallel and sequential QR and LU factorizations: theory and practice
James Demmel, Laura Grigori, Mark Hoemmen +1
We present parallel and sequential dense QR factorization algorithms that are both optimal (up to polylogarithmic factors) in the amount of communication they perform, and just as…
Accurate and Efficient Expression Evaluation and Linear Algebra
James Demmel, Ioana Dumitriu, Olga Holtz +1
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with st…
Fast linear algebra is stable
James Demmel, Ioana Dumitriu, Olga Holtz
In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of -by-…
Fast matrix multiplication is stable
James Demmel, Ioana Dumitriu, Olga Holtz +1
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix mu…
Toward accurate polynomial evaluation in rounded arithmetic
James Demmel, Ioana Dumitriu, Olga Holtz
Given a multivariate real (or complex) polynomial and a domain , we would like to decide whether an algorithm exists to evaluate accurately for all $x \in {\cal…
The complexity of accurate floating point computation
James Demmel
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizatio…