10 papers
Dimension-independent eigenvalue approximation for sparse matrices
Natalia Hajlasz, Christopher Musco, Jonathan Weare +1
Many applications in science and engineering require solving sparse Hermitian eigenvalue problems that are so large that even algorithms whose runtime scales linearly with the matr…
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…
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…
Almost Navigable Graphs
Pratyush Avi, Christopher Musco
Graph-based methods like HNSW, DiskANN, NSG, and others have become an increasingly popular choice for implementing approximate nearest neighbor search (ANNS) in Vector Databases (…
An Exact Algorithm for the Unanimous Vote Problem
Feyza Duman Keles, Lisa Hellerstein, Kunal Marwaha +2
Consider independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we…
Does block size matter in randomized block Krylov low-rank approximation?
Tyler Chen, Ethan N. Epperly, Raphael A. Meyer +2
We study the problem of computing a rank- approximation of a matrix using randomized block Krylov iteration. Prior work has shown that, for block size or , a $(1…
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…