19 papers
A new analysis of the randomly pivoted Cholesky algorithm
Ethan N. W. Epperly
The randomly pivoted Cholesky algorithm is one of the leading methods for computing a low-rank approximation to a large positive-semidefinite matrix. However, while it consistently…
Lonic: Algorithm-Hardware Co-Design for Energy-Efficient Fully Local Online SNN Training with INT4 Precision
Peilin Chen, Xiaoxuan Yang
Spiking neural networks (SNNs) have recently attracted increasing attention as an energy-efficient learning paradigm. Existing works also propose temporally and fully local online…
The matrix-vector complexity of
MichaÅ DereziÅski, Ethan N. Epperly, Raphael A. Meyer
Matrix--vector algorithms, particularly Krylov subspace methods, are widely viewed as the most effective algorithms for solving large systems of linear equations. This paper establ…
Linear algebra at exponential scale via tensor network dimension reduction
Chris Camaño, Ethan N. Epperly, Raphael A. Meyer +1
Many problems in modern scientific computing are challenging because of a \emph{curse of dimension}, where their mathematical formulation involves objects whose dimension is \emph{…
Sharp analysis of sketched least squares and randomized low-rank approximation
Ethan N. Epperly, Robert J. Webber
Two widely used randomized algorithms are the sketch-and-solve method for least-squares regression and the randomized SVD for low-rank approximation. These algorithms apply a rando…
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…