5 papers
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 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…
Quantifying Epistemic Uncertainty in Diffusion Models
Aditi Gupta, Raphael A. Meyer, Yotam Yaniv +2
To ensure high quality outputs, it is important to quantify the epistemic uncertainty of diffusion models. Existing methods are often unreliable because they mix epistemic and alea…
Faster Linear Algebra Algorithms with Structured Random Matrices
Chris Camaño, Ethan N. Epperly, Raphael A. Meyer +1
To achieve the greatest possible speed, practitioners regularly implement randomized algorithms for low-rank approximation and least-squares regression with structured dimension re…
Debiasing Polynomial and Fourier Regression
Chris Camaño, Raphael A. Meyer, Kevin Shu
We study the problem of approximating an unknown function by a degree- polynomial using as few function evaluations as possible, where error is measu…