16 citations · 81 across the 20 of their papers we have counts for
20 papers
A simple stability analysis of the Lanczos algorithm in finite precision arithmetic
Tyler Chen
We give a self-contained analysis of the symmetric Lanczos algorithm without reorthogonalization when computations are performed inexactly. We show the computed Lanczos vectors are…
The Lanczos algorithm for matrix functions: a handbook for scientists
Tyler Chen
Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulti…
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…
Fixed-sparsity matrix approximation from matrix-vector products
Noah Amsel, Tyler Chen, Feyza Duman Keles +3
We study the problem of approximating a matrix with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when is accessed only by ma…
A spectrum adaptive kernel polynomial method
Tyler Chen
The kernel polynomial method (KPM) is a powerful numerical method for approximating spectral densities. Typical implementations of the KPM require an a prior estimate for an interv…
Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm
Tyler Chen, Anne Greenbaum, Natalie Wellen
Given an by matrix and an -vector , along with a rational function , we show how to find the optimal approximation to from the K…
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices
Tyler Chen, Anne Greenbaum, Thomas Trogdon
We study the GMRES algorithm applied to linear systems of equations involving a scaled and shifted matrix whose entries are independent complex Gaussians. When the righ…
Nearly Optimal Approximation of Matrix Functions by the Lanczos Method
Noah Amsel, Tyler Chen, Anne Greenbaum +2
Approximating the action of a matrix function on a vector is an increasingly important primitive in machine learning, data science, and statistics, wit…
Stability of the Lanczos algorithm on matrices with regular spectral distributions
Tyler Chen, Thomas Trogdon
We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polyno…
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…
Analysis of stochastic Lanczos quadrature for spectrum approximation
Tyler Chen, Thomas Trogdon, Shashanka Ubaru
The cumulative empirical spectral measure (CESM) of a symmetric matrix is defined as the fraction of eigenvalues of…
Error bounds for Lanczos-based matrix function approximation
Tyler Chen, Anne Greenbaum, Cameron Musco +1
We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm for computing when is a Hermitian matri…
Non-asymptotic moment bounds for random variables rounded to non-uniformly spaced sets
Tyler Chen
We study the effects of rounding on the moments of random variables. Specifically, given a random variable and its rounded counterpart , we study $|\mathb…
On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic
Anne Greenbaum, Hexuan Liu, Tyler Chen
We consider three mathematically equivalent variants of the conjugate gradient (CG) algorithm and how they perform in finite precision arithmetic. It was shown in [{\em Behavior of…
Predict-and-recompute conjugate gradient variants
Tyler Chen, Erin C. Carson
The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions require…