This paper presents square root information smoothing (SRIS) as a more efficient and accurate alternative to the extended Kalman filter (EKF) for solving the simultaneous localization and mapping (SLAM) problem. SRIS leverages square root factorization of the information matrix or measurement matrix to maintain sparsity, which leads to faster, more accurate, and more stable computations. Unlike the EKF, which becomes computationally impractical for large environments, SRIS can handle non-linear models and provides the entire robot trajectory at lower cost. It also automatically exploits the locality inherent in SLAM problems through column ordering heuristics. The paper introduces the theory behind SRIS, interprets it in terms of graphical models, and presents simulation results demonstrating its effectiveness. It compares SRIS with the EKF and shows that SRIS outperforms the EKF in terms of speed, accuracy, and computational efficiency, especially for large-scale problems. The paper also discusses the use of square root SAM (SRAM) in both batch and incremental modes, highlighting its ability to handle sparse matrices and its potential for further optimization through domain-specific knowledge. The paper also explores the use of Cholesky and QR factorizations in solving the least squares problem associated with SLAM. It shows that QR factorization is more accurate and numerically stable than Cholesky, but Cholesky is faster for sparse matrices. The paper compares the performance of different factorization methods, including sparse LDL, Cholesky, and QR, and finds that sparse LDL performs best in practice. The paper concludes that SRIS is a promising approach for SLAM, offering significant advantages over the EKF, including exactness, efficiency, and the ability to handle large-scale problems. It also suggests that further research is needed to improve the performance of SRIS, particularly in terms of computational complexity and the integration of domain knowledge. The paper also highlights the importance of sparse matrix representations and efficient factorization algorithms in the context of SLAM.This paper presents square root information smoothing (SRIS) as a more efficient and accurate alternative to the extended Kalman filter (EKF) for solving the simultaneous localization and mapping (SLAM) problem. SRIS leverages square root factorization of the information matrix or measurement matrix to maintain sparsity, which leads to faster, more accurate, and more stable computations. Unlike the EKF, which becomes computationally impractical for large environments, SRIS can handle non-linear models and provides the entire robot trajectory at lower cost. It also automatically exploits the locality inherent in SLAM problems through column ordering heuristics. The paper introduces the theory behind SRIS, interprets it in terms of graphical models, and presents simulation results demonstrating its effectiveness. It compares SRIS with the EKF and shows that SRIS outperforms the EKF in terms of speed, accuracy, and computational efficiency, especially for large-scale problems. The paper also discusses the use of square root SAM (SRAM) in both batch and incremental modes, highlighting its ability to handle sparse matrices and its potential for further optimization through domain-specific knowledge. The paper also explores the use of Cholesky and QR factorizations in solving the least squares problem associated with SLAM. It shows that QR factorization is more accurate and numerically stable than Cholesky, but Cholesky is faster for sparse matrices. The paper compares the performance of different factorization methods, including sparse LDL, Cholesky, and QR, and finds that sparse LDL performs best in practice. The paper concludes that SRIS is a promising approach for SLAM, offering significant advantages over the EKF, including exactness, efficiency, and the ability to handle large-scale problems. It also suggests that further research is needed to improve the performance of SRIS, particularly in terms of computational complexity and the integration of domain knowledge. The paper also highlights the importance of sparse matrix representations and efficient factorization algorithms in the context of SLAM.