4 papers · 1 filter
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…
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…