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Towards Universal Convergence of Backward Error in Linear System Solvers
MichaÅ DereziÅski, Yuji Nakatsukasa, Elizaveta Rebrova
The quest for an algorithm that solves an linear system in time complexity, or when solving up to relative error, is a long-sta…
Numerical Instabilities in the Kaczmarz Method and Stabilization by Iterative Refinement
MichaÅ DereziÅski, Ethan N. Epperly, Deanna Needell +1
The randomized Kaczmarz method and its accelerated variants are a powerful class of iterative methods for solving large-scale linear systems, offering guaranteed convergence with l…
Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation
Shabarish Chenakkod, MichaÅ DereziÅski
The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, t…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +36
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
Randomized Kaczmarz Methods with Beyond-Krylov Convergence
MichaÅ DereziÅski, Deanna Needell, Elizaveta Rebrova +1
Randomized Kaczmarz methods form a family of linear system solvers which converge by repeatedly projecting their iterates onto randomly sampled equations. While effective in some c…