4 papers
Stable Matrix-Free Q-less QR via Preconditioning and Randomization
Oleg Balabanov, Maksim Melnichenko, Michael W. Mahoney
This article develops matrix-free Q-less QR algorithms for orthogonalizing tall linear operators. Our main algorithm, CQRRTO, uses randomized preconditioning to make a single Chole…
Preconditioning via Randomized Range Deflation (RandRAND)
Oleg Balabanov, Caleb Ju, Kaiwen He +2
We introduce RandRAND, a new class of randomized preconditioning methods for large-scale linear systems. RandRAND deflates the spectrum via efficient orthogonal projections onto ra…
Anatomy of High-Performance Column-Pivoted QR Decomposition
Maksim Melnichenko, Riley Murray, William Killian +4
We introduce an algorithmic framework for performing QR factorization with column pivoting (QRCP) on general matrices. The framework enables the design of practical QRCP algorithms…
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…