The matrix sign function algorithm underlies most parallel algorithms for solving the algebraic Riccati equation (ARE). The method is not always numerically backward stable, however. When combined with an iterative refinement loop it stably solves a large class of AREs, but it fails on some problems that are easily solved by other methods.
The goal of this research is a sign-function-based ARE solver that is backward stable. The result is a scaling strategy, a shifting technique, and carefully chosen stopping criteria which together overcome most of the instabilities in the basic algorithm. Computational experiments demonstrate the practical effectiveness of the algorithm enhancements.
For the entire collection see [Zbl 0809.00014].