6 papers · 1 filter
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…
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…
Everything is Vecchia: Unifying low-rank and sparse inverse Cholesky approximations
Eagan Kaminetz, Robert J. Webber
The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with…
Keep the beat going: Automatic drum transcription with momentum
Alisha L. Foster, Robert J. Webber
How can we process a piece of recorded music to detect and visualize the onset of each instrument? A simple, interpretable approach is based on partially fixed nonnegative matrix f…
Randomized Kaczmarz with tail averaging
Ethan N. Epperly, Gil Goldshlager, Robert J. Webber
The randomized Kaczmarz (RK) method is a well-known approach for solving linear least-squares problems with a large number of rows. RK accesses and processes just one row at a time…
Embrace rejection: Kernel matrix approximation by accelerated randomly pivoted Cholesky
Ethan N. Epperly, Joel A. Tropp, Robert J. Webber
Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper devel…