5 papers · 1 filter
Minimizing the Arithmetic and Communication Complexity of Jacobi's Method for Eigenvalues and Singular Values: Part Two -- Parallel Algorithms
James Demmel, Hengrui Luo, Ryan Schneider +1
This paper presents several parallel versions of Jacobi's method for the symmetric eigenvalue problem and the SVD. A continuation of [Demmel, Luo, Schneider, & Wang 2025], we devel…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
Minimizing the Arithmetic and Communication Complexity of Jacobi's Method for Eigenvalues and Singular Values: Part One -- Serial Algorithms
James Demmel, Hengrui Luo, Ryan Schneider +1
We analyze several versions of Jacobi's method for the symmetric eigenvalue problem. Our goal is to reduce the asymptotic cost of the algorithm as much as possible, as measured by…
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…