Lanczos-like method for the time-ordered exponential
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The time-ordered exponential is defined as the function that solves any system of coupled first order linear differential equations with constant or non-constant coefficients. In spite of it being at the heart of much system dynamics, control theory and model reduction problems, the time-ordered exponential function remains elusively difficult to evaluate. Here 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 natural strategy for its numerical implementation is also outlined and will form the basis of a future work.
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