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math.NA2026
Convergence rates of randomly pivoted methods for low-rank approximation
Ryan Divan, Marc Aurèle Gilles
Randomly pivoted Cholesky, QR, and LU are iterative algorithms that form structured low-rank approximations of a matrix by sampling columns, or rows and columns, from the residual.…
math.NA2026
Convergence rates for pivoted QR and LU
Marc Aurèle Gilles
Pivoted QR and pivoted LU decompositions are greedy algorithms used to compute low-rank approximations of matrices from selected columns, or selected rows and columns. Despite thei…
math.NA2026
Low-Rank Approximation by Randomly Pivoted LU
Marc Aurèle Gilles, Heather Wilber
The low-rank approximation properties of Randomly Pivoted LU (RPLU), a variant of Gaussian elimination where pivots are sampled proportional to the squared entries of the Schur com…