# Numerical Investigation of Newton’s Method for Solving Discrete-time Algebraic Riccati Equations

### Vasile Sima, Peter Benner

#### Abstract

A Newton-like algorithm and some line search strategies for solving discrete-time algebraic Riccati equations are discussed. Algorithmic and implementation details incorporated in the developed solver are described. Some numerical results of an extensive performance investigation on a large collection of examples are summarized. These results often show significantly improved accuracy, measured in terms of normalized and relative residuals, in comparison with the state-of-the-art MATLAB function. The new solver is strongly recommended for improving the solutions computed by other solvers.

Download#### Paper Citation

#### in Harvard Style

Sima V. and Benner P. (2018). **Numerical Investigation of Newton’s Method for Solving Discrete-time Algebraic Riccati Equations**.In *Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-321-6, pages 66-75. DOI: 10.5220/0006860600660075

#### in Bibtex Style

@conference{icinco18,

author={Vasile Sima and Peter Benner},

title={Numerical Investigation of Newton’s Method for Solving Discrete-time Algebraic Riccati Equations},

booktitle={Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2018},

pages={66-75},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006860600660075},

isbn={978-989-758-321-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Numerical Investigation of Newton’s Method for Solving Discrete-time Algebraic Riccati Equations

SN - 978-989-758-321-6

AU - Sima V.

AU - Benner P.

PY - 2018

SP - 66

EP - 75

DO - 10.5220/0006860600660075