A Unified Low-rank ADI Framework with Shared Linear Solves for Simultaneously Solving Multiple Lyapunov, Sylvester, and Riccati Equations

These MATLAB codes implement the Unified ADI Framework with self-generating shifts. The framework can simultaneously handle multiple Lyapunov, Sylvester, and Riccati equations, as well as several model reduction tasks. It does not require dedicated shifted linear solves; instead, it reuses linear solves across the problems, offering a significantly better return on the computational cost of each solve. The algorithm is fully automatic and determines all free parameters on its own, without any user intervention.