# Using LDLT factorizations in Newton's method for solving general large-scale algebraic Riccati equations

arXiv: https://arxiv.org/abs/2402.06844 · HTML: https://mlsanity.com/paper/2402.06844/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback design](https://mlsanity.com/paper/2403.18044/) (2024)

## Abstract (arXiv)

Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati equation. This is not the case when it comes to large-scale sparse coefficient matrices. In this paper, we provide a reformulation of the Newton-Kleinman iteration scheme for continuous-time algebraic Riccati equations using indefinite symmetric low-rank factorizations. This allows the application of the method to the case of general large-scale sparse coefficient matrices. We provide convergence results for several prominent realizations of the equation and show in numerical examples the effectiveness of the approach.