This paper introduces Square Root Information Smoothing (SRIS) as an alternative to the Extended Kalman Filter (EKF) for solving the Simultaneous Localization and Mapping (SLAM) problem. SRIS factorizes either the information matrix or the measurement matrix into a square root form, offering several advantages over EKF, including faster computation, better handling of non-linear models, and the ability to recover the entire robot trajectory at a lower cost. The authors present the theoretical foundation of SRIS, its interpretation in terms of graphical models, and simulation results demonstrating its practical potential. They also discuss the benefits of column ordering heuristics in exploiting the sparsity inherent in SLAM problems, which can significantly reduce computational complexity. The paper concludes by highlighting the practical interest of SRIS in the SLAM community, noting its exactness and performance even in sub-optimal incremental schemes. However, further work is needed to establish complexity bounds and compare the approach with other SLAM variants.This paper introduces Square Root Information Smoothing (SRIS) as an alternative to the Extended Kalman Filter (EKF) for solving the Simultaneous Localization and Mapping (SLAM) problem. SRIS factorizes either the information matrix or the measurement matrix into a square root form, offering several advantages over EKF, including faster computation, better handling of non-linear models, and the ability to recover the entire robot trajectory at a lower cost. The authors present the theoretical foundation of SRIS, its interpretation in terms of graphical models, and simulation results demonstrating its practical potential. They also discuss the benefits of column ordering heuristics in exploiting the sparsity inherent in SLAM problems, which can significantly reduce computational complexity. The paper concludes by highlighting the practical interest of SRIS in the SLAM community, noting its exactness and performance even in sub-optimal incremental schemes. However, further work is needed to establish complexity bounds and compare the approach with other SLAM variants.