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math.NA2025
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…
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…