On the tridiagonalization of systems of coupled linear differential equations
Pierre-Louis Giscard, Stefano Pozza · arXiv (Cornell University) · 2020
Under what conditions can one tridiagonalize a system of coupled linear differential equations with non-constant coefficients by appealing only to `well-behaved' distributions? In this work we show that if all the non-constant coefficients are smooth functions then tridiagonalisation is always possible using only piecewise smooth functions and isolated Dirac delta distributions. As a corollary, we formally establish the convergence and good behavior of the recently published Lanczos-like algorithm for solving arbitrary linear differential systems with smooth coefficients via tridiagonalization. This is a key piece in evaluating the hitherto elusively difficult ordered exponential function, both formally and numerically.