RAILS | Residual Approximation-based Iterative Lyapunov Solver

RAILS is a C++ library. RAILS has no bugs, it has a Permissive License and it has low support. However RAILS has 8 vulnerabilities. You can download it from GitHub.

RAILS is an iterative solver for generalized continuous time Lyapunov equations. These equations are of the form. where ' denotes the transpose, A and M are mxm, X is mxm and symmetric, and B is mxn where n << m. We solve for a low-rank approximation of X of the form X=V*T*V'. The method work by expanding the search space in every iteration by eigenvectors of the residual. Unlike many other methods, this method can be restarted, and therefore can limit the size of the search space. It is especially well suited when one wants to perform multiple computations on similar systems since then one can use the approximate solution from the previous computation as an initial guess (for instance in a continuation), or when n is relatively large since we can use any amount of eigenvectors of the residual to expand the space (as long as it's smaller or equal to n). This repository contains both a C++ and a Matlab implementation of the algorithm.