16 citations · 81 across the 20 of their papers we have counts for
6 papers · 1 filter
A posteriori error bounds for the block-Lanczos method for matrix function approximation
Qichen Xu, Tyler Chen
We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments…
On the fast convergence of minibatch heavy ball momentum
Raghu Bollapragada, Tyler Chen, Rachel Ward
Simple stochastic momentum methods are widely used in machine learning optimization, but their good practical performance is at odds with an absence of theoretical guarantees of ac…
Krylov-aware stochastic trace estimation
Tyler Chen, Eric Hallman
We introduce an algorithm for estimating the trace of a matrix function using implicit products with a symmetric matrix . Existing methods for implicit…
Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
Tyler Chen, Yu-Chen Cheng
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to…
Randomized matrix-free quadrature: unified and uniform bounds for stochastic Lanczos quadrature and the kernel polynomial method
Tyler Chen, Thomas Trogdon, Shashanka Ubaru
We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanc…
Low-memory Krylov subspace methods for optimal rational matrix function approximation
Tyler Chen, Anne Greenbaum, Cameron Musco +1
We describe a Lanczos-based algorithm for approximating the product of a rational matrix function with a vector. This algorithm, which we call the Lanczos method for optimal ration…