A Lanczos-like method for the time-ordered exponential

The time-ordered exponential is defined as the function that solves a system of coupled first-order linear differential equations with generally non-constant coefficients. In spite of being at the heart of much system dynamics, control theory, and model reduction problems, the time-ordered exponential function remains elusively difficult to evaluate. In the talk, we present a Lanczos-like algorithm capable of evaluating it by producing a tridiagonalization of the original differential system. The algorithm is presented in a theoretical setting. Nevertheless, a strategy for its numerical implementation is also outlined and will be subject of future investigation.