activity
20032025
most citedFast linear algebra is stable

150 citations · 367 across the 12 of their papers we have counts for

collaborators

12 papers

math.NA2025

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…

math.NA2023

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…

math.NA2023★ 3 cited

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…

math.NA2023★ 17 cited

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…

math.NA2023★ 3 cited

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…

math.NA2019★ 4 cited

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…

math.NA2008★ 19 cited

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…

math.NA2007★ 76 cited

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…

math.NA2006★ 150 cited

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-…

math.NA2006★ 80 cited

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…

math.NA2005★ 11 cited

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…

math.NA2003★ 4 cited

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…