# Square Root Bundle Adjustment for Large-Scale Reconstruction

arXiv: https://arxiv.org/abs/2103.01843 · HTML: https://mlsanity.com/paper/2103.01843/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 36 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 2 of 2)

- [Stochastic Bundle Adjustment for Efficient and Scalable 3D Reconstruction](https://mlsanity.com/paper/2008.00446/) (2020)
- [Distributed Bundle Adjustment](https://mlsanity.com/paper/1708.07954/) (2017)

## Built on by (most cited first, 14 of 14)

- [MegBA: A GPU-Based Distributed Library for Large-Scale Bundle Adjustment](https://mlsanity.com/paper/2112.01349/) (2021)
- [Power Variable Projection for Initialization-Free Large-Scale Bundle Adjustment](https://mlsanity.com/paper/2405.05079/) (2024)
- [Square Root Marginalization for Sliding-Window Bundle Adjustment](https://mlsanity.com/paper/2109.02182/) (2021)
- [SchurVINS: Schur Complement-Based Lightweight Visual Inertial Navigation System](https://mlsanity.com/paper/2312.01616/) (2023)
- [Efficient Second-Order Plane Adjustment](https://mlsanity.com/paper/2211.11542/) (2022)
- [A Game of Bundle Adjustment -- Learning Efficient Convergence](https://mlsanity.com/paper/2308.13270/) (2023)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [A Pose-only Geometric Constraint for Multi-Camera Pose Adjustment](https://mlsanity.com/paper/2604.23704/) (2026)
- [Quantum Levenberg--Marquardt Algorithm for optimization in Bundle Adjustment](https://mlsanity.com/paper/2203.02311/) (2022)
- [A Saddle Point Remedy: Power of Variable Elimination in Non-convex Optimization](https://mlsanity.com/paper/2511.01234/) (2025)
- [CSS-BA: Gate-Guided Column Space Search for Bundle Adjustment](https://mlsanity.com/paper/2607.15652/) (2026)
- [Stable and Scalable Bundle Adjustment of Holistic 3D Structures](https://mlsanity.com/paper/2609.04026/) (2026)
- [Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery](https://mlsanity.com/paper/2610.06978/) (2026)
- [RootSLAM: Square Root Bundle Adjustment for Visual-Inertial SLAM](https://mlsanity.com/paper/2610.15157/) (2026)

## Abstract (arXiv)

We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to the commonly used Schur complement trick, improves the numeric stability of computations, and allows for solving large-scale bundle adjustment problems with single-precision floating-point numbers. We show in real-world experiments with the BAL datasets that even in single precision the proposed solver achieves on average equally accurate solutions compared to Schur complement solvers using double precision. It runs significantly faster, but can require larger amounts of memory on dense problems. The proposed formulation relies on simple linear algebra operations and opens the way for efficient implementations of bundle adjustment on hardware platforms optimized for single-precision linear algebra processing.