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math.NA2026
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…
math.NA2025
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…
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…