Recorded 03 April 2025. Alice Cortinovis of Stanford University presents "Numerical approximation of traces of matrix functions" at IPAM's Optimal Transport for Density Operators: Theory and Numerics Workshop. Abstract: In this talk, we consider the problem of numerically computing (or approximating) the trace of a matrix function f(A). Important examples include the matrix logarithm, the entropy, and the exponential, which play key roles in quantum optimal transport formulations. We will present an overview of numerical linear algebra techniques to approximate such traces efficiently. In particular, we describe the Hutchinson trace estimator -- a stochastic algorithm that approximates the trace using quadratic forms involving the matrix and some random vectors -- and some variants including partial trace approximation and variance reduction techniques. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-optimal-transport-for-density-operators-theory-and-numerics/?tab=schedule