We introduce an algorithm for estimating the trace of a matrix function using implicit products
with a symmetric matrix. Existing methods for implicit trace estimation of a matrix function …

We present a new sublinear time algorithm for approximating the spectral density
(eigenvalue distribution) of an n× n normalized graph adjacency or Laplacian matrix. The …

This article presents a randomized matrix-free method for approximating the trace of f (A),
where A is a large symmetric matrix and f is a function analytic in a closed interval containing …

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 a set …

We study lower bounds for the problem of approximating a one dimensional distribution
given (noisy) measurements of its moments. We show that there are distributions on $[-1, 1] …

We study randomized matrix-free quadrature algorithms for spectrum and spectral sum
approximation. The algorithms studied are characterized by the use of a Krylov subspace …

We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form ym= ϕ
(x) y^m=ϕ(x) in R 2 R^2 where m= 1, 2 m=1,2 and ϕ is a polynomial of arbitrary degree d, in …

We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative
algorithm for computing (f (A) b) when (A) is a Hermitian matrix and (b) is a given vector …

In this paper, we present a quantum algorithm for approximating multivariate traces, ie the
traces of matrix products. Our research is motivated by the extensive utility of multivariate …

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 …