Department of Mathematics

This talk considers the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix \( A \), defined as \( \mbox{tr}(f(A)) \) where \( f(x) =-x\log x \)

We employ both polynomial and rational Krylov subspace algorithms within two types of approximation methods, namely, randomized trace estimators and probing techniques based on graph colorings.

Error bounds and heuristics are developed to guide and enhance the implementation of these algorithms.