10 papers
Hutch#: Optimal non-adaptive Frobenius norm estimation
Tyler Chen, Diana Halikias, Christopher Musco +1
The Girard--Hutchinson estimator provides an extremely simple randomized estimate of the Frobenius norm of a matrix that can only be accessed implicitly via matrix-vector produ…
Optimal near-optimality bounds for the Lanczos method for matrix functions
Tyler Chen, David Persson
Let be Hermitian positive definite and let denote the Lanczos approximation to . We prove that if or is Stieltjes, then the -norm error of t…
A recursive butterfly factorization with optimality guarantees
David Persson, Paul G. Beckman, Tyler Chen +2
We formalize a recursive format for representing a butterfly matrix. This new format naturally leads to a simple recursive algorithm for computing a quasi-optimal butterfly approxi…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
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…
Query Efficient Structured Matrix Learning
Noah Amsel, Pratyush Avi, Tyler Chen +5
We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix given access to matrix-vector product (matvec) queries of the…
Quasi-optimal hierarchically semi-separable matrix approximation
Noah Amsel, Tyler Chen, Feyza Duman Keles +4
We present a randomized algorithm for producing a quasi-optimal hierarchically semi-separable (HSS) approximation to an matrix using only matrix-vector products wit…
The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm
Noah Amsel, David Persson, Christopher Musco +1
Computing the polar decomposition and the related matrix sign function has been a well-studied problem in numerical analysis for decades. Recently, it has emerged as an important s…
Randomized block-Krylov subspace methods for low-rank approximation of matrix functions
David Persson, Tyler Chen, Christopher Musco
The randomized SVD is a method to compute an inexpensive, yet accurate, low-rank approximation of a matrix. The algorithm assumes access to the matrix through matrix-vector product…
Near-optimal hierarchical matrix approximation from matrix-vector products
Tyler Chen, Feyza Duman Keles, Diana Halikias +3
We describe a randomized algorithm for producing a near-optimal hierarchical off-diagonal low-rank (HODLR) approximation to an matrix , accessible only thou…
Algorithm-agnostic low-rank approximation of operator monotone matrix functions
David Persson, Raphael A. Meyer, Christopher Musco
Low-rank approximation of a matrix function, , is an important task in computational mathematics. Most methods require direct access to , which is often considerably mo…