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math.NA2026
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…
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.NA2023
CholeskyQR with Randomization and Pivoting for Tall Matrices (CQRRPT)
Maksim Melnichenko, Oleg Balabanov, Riley Murray +3
This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with many more rows than columns. The algorithm carefully…