On the Solution of Large-scale Non-autonomous Differential Riccati Equations: a Numerical Study

Mathematics > Numerical Analysis [Submitted on 16 Jun 2026] Title:On the Solution of Large-scale Non-autonomous Differential Riccati Equations: a Numerical Study View PDF HTML (experimental)Abstract:We explore the numerical solution of large-scale non-autonomous Differential Riccati Equations (DREs). While we assume to discretize the differential operator using a Backward Differentiation Formula (BDF) of order s, we solve the generalized Algebraic Riccati Equation (gARE) resulting at each time step by different state-of-the-art methods. In particular, we compare the performance of the inexact Newton- Kleinman method with line search and the low-rank RADI iteration, considering for both methods two different initialization strategies: zero initialization and warm-start. A comprehensive panel of numerical results illustrate the potential and limitations of these methods when employed within a numerical pipeline for the solution of DREs, rather than for the isolated solution of a single gARE, as commonly considered in the existing literature. Current browse context: math.NA References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.