| .. _sec-bibliography: | |
| ============ | |
| Bibliography | |
| ============ | |
| Background Reading | |
| ================== | |
| For a short, informative introduction to non-linear least squares, we | |
| recommend the booklet by [Madsen]_. For a general introduction to | |
| non-linear optimization, we recommend [NocedalWright]_. [Bjorck]_ | |
| remains the seminal reference on least squares problems. | |
| [TrefethenBau]_ is our favorite text on introductory numerical linear | |
| algebra. [Triggs]_ provides a thorough treatment of the bundle | |
| adjustment problem. | |
| References | |
| ========== | |
| .. [Agarwal] S. Agarwal, N. Snavely, S. M. Seitz, and R. Szeliski, | |
| **Bundle Adjustment in the Large**, *Proceedings of the European | |
| Conference on Computer Vision*, pp. 29--42, 2010. | |
| .. [Bjorck] Å. Björck, **Numerical Methods for Least Squares | |
| Problems**, SIAM, 1996. | |
| .. [Brown] D. C. Brown, **A Solution to the General Problem of | |
| Multiple Station Analytical Stereo Triangulation**, Technical | |
| Report 43, Patrick Air Force Base, Florida, 1958. | |
| .. [ByrdNocedal] R. H. Byrd, J. Nocedal, and R. B. Schnabel, | |
| **Representations of Quasi-Newton Matrices and Their Use in Limited | |
| Memory Methods**, *Mathematical Programming*, 63(1--3):129--156, 1994. | |
| .. [ByrdSchnabel] R. H. Byrd, R. B. Schnabel, and G. A. Shultz, | |
| **Approximate Solution of the Trust Region Problem by Minimization | |
| over Two-Dimensional Subspaces**, *Mathematical Programming*, | |
| 40(1):247--263, 1988. | |
| .. [Chen] Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam, | |
| **Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization | |
| and Update/Downdate**, *ACM Transactions on Mathematical Software*, | |
| 35(3), 2008. | |
| .. [Conn] A. R. Conn, N. I. M. Gould, and P. L. Toint, **Trust-Region | |
| Methods**, SIAM, 2000. | |
| .. [Davis] T. A. Davis, **Direct Methods for Sparse Linear Systems**, | |
| SIAM, 2006. | |
| .. [Dellaert] F. Dellaert, J. Carlson, V. Ila, K. Ni, and C. E. Thorpe, | |
| **Subgraph-Preconditioned Conjugate Gradients for Large Scale SLAM**, | |
| *IEEE/RSJ International Conference on Intelligent Robots and | |
| Systems*, 2010. | |
| .. [GolubPereyra] G. H. Golub and V. Pereyra, **The Differentiation of | |
| Pseudo-Inverses and Nonlinear Least Squares Problems Whose | |
| Variables Separate**, *SIAM Journal on Numerical Analysis*, | |
| 10(2):413--432, 1973. | |
| .. [GouldScott] N. Gould and J. Scott, **The State-of-the-Art of | |
| Preconditioners for Sparse Linear Least-Squares Problems**, | |
| *ACM Transactions on Mathematical Software*, 43(4), 2017. | |
| .. [HartleyZisserman] R. I. Hartley and A. Zisserman, **Multiple View | |
| Geometry in Computer Vision**, Cambridge University Press, 2004. | |
| .. [Hertzberg] C. Hertzberg, R. Wagner, U. Frese, and L. Schröder, | |
| **Integrating Generic Sensor Fusion Algorithms with Sound State | |
| Representations through Encapsulation of Manifolds**, *Information | |
| Fusion*, 14(1):57--77, 2013. | |
| .. [KanataniMorris] K. Kanatani and D. D. Morris, **Gauges and Gauge | |
| Transformations for Uncertainty Description of Geometric Structure | |
| with Indeterminacy**, *IEEE Transactions on Information Theory*, | |
| 47(5):2017--2028, 2001. | |
| .. [Keys] R. G. Keys, **Cubic Convolution Interpolation for Digital | |
| Image Processing**, *IEEE Transactions on Acoustics, Speech, and | |
| Signal Processing*, 29(6), 1981. | |
| .. [KushalAgarwal] A. Kushal and S. Agarwal, **Visibility Based | |
| Preconditioning for Bundle Adjustment**, *Proceedings of the IEEE | |
| Conference on Computer Vision and Pattern Recognition*, 2012. | |
| .. [Kanzow] C. Kanzow, N. Yamashita, and M. Fukushima, | |
| **Levenberg-Marquardt Methods with Strong Local Convergence | |
| Properties for Solving Nonlinear Equations with Convex | |
| Constraints**, *Journal of Computational and Applied Mathematics*, | |
| 172(2):375--397, 2004. | |
| .. [Levenberg] K. Levenberg, **A Method for the Solution of Certain | |
| Non-Linear Problems in Least Squares**, *Quarterly of Applied | |
| Mathematics*, 2(2):164--168, 1944. | |
| .. [LiSaad] N. Li and Y. Saad, **MIQR: A Multilevel Incomplete QR | |
| Preconditioner for Large Sparse Least Squares Problems**, *SIAM | |
| Journal on Matrix Analysis and Applications*, 28(2):524--550, 2006. | |
| .. [LourakisArgyros] M. I. A. Lourakis and A. A. Argyros, **Is | |
| Levenberg-Marquardt the Most Efficient Optimization Algorithm for | |
| Implementing Bundle Adjustment?**, *Proceedings of the IEEE | |
| International Conference on Computer Vision*, 2005. | |
| .. [Madsen] K. Madsen, H. B. Nielsen, and O. Tingleff, **Methods for | |
| Non-Linear Least Squares Problems**, 2004. | |
| .. [Mandel] J. Mandel, **On Block Diagonal and Schur Complement | |
| Preconditioning**, *Numerische Mathematik*, 58(1):79--93, 1990. | |
| .. [Marquardt] D. W. Marquardt, **An Algorithm for Least-Squares | |
| Estimation of Nonlinear Parameters**, *Journal of the Society for | |
| Industrial and Applied Mathematics*, 11(2):431--441, 1963. | |
| .. [Mathew] T. P. A. Mathew, **Domain Decomposition Methods for the | |
| Numerical Solution of Partial Differential Equations**, Springer, | |
| 2008. | |
| .. [NashSofer] S. G. Nash and A. Sofer, **Assessing a Search Direction | |
| Within a Truncated Newton Method**, *Operations Research Letters*, | |
| 9(4):219--221, 1990. | |
| .. [Nocedal] J. Nocedal, **Updating Quasi-Newton Matrices with Limited | |
| Storage**, *Mathematics of Computation*, 35(151):773--782, 1980. | |
| .. [NocedalWright] J. Nocedal and S. J. Wright, **Numerical | |
| Optimization**, Springer, 2006. | |
| .. [Oren] S. S. Oren, **Self-Scaling Variable Metric (SSVM) Algorithms | |
| Part II: Implementation and Experiments**, *Management Science*, | |
| 20(5):863--874, 1974. | |
| .. [Press] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and | |
| B. P. Flannery, **Numerical Recipes**, Cambridge University Press, | |
| 2007. | |
| .. [Ridders] C. J. F. Ridders, **Accurate Computation of F'(x) and | |
| F'(x) F"(x)**, *Advances in Engineering Software*, 4(2):75--76, | |
| 1982. | |
| .. [RuheWedin] A. Ruhe and P. Å. Wedin, **Algorithms for Separable | |
| Nonlinear Least Squares Problems**, *SIAM Review*, 22(3):318--337, | |
| 1980. | |
| .. [Saad] Y. Saad, **Iterative Methods for Sparse Linear Systems**, | |
| SIAM, 2003. | |
| .. [Simon] I. Simon, N. Snavely, and S. M. Seitz, **Scene Summarization | |
| for Online Image Collections**, *Proceedings of the IEEE | |
| International Conference on Computer Vision*, 2007. | |
| .. [Stigler] S. M. Stigler, **Gauss and the Invention of Least | |
| Squares**, *The Annals of Statistics*, 9(3):465--474, 1981. | |
| .. [TenenbaumDirector] J. Tennenbaum and B. Director, **How Gauss | |
| Determined the Orbit of Ceres**, *Fidelio*, 7(2):4--88, 1998. | |
| .. [TrefethenBau] L. N. Trefethen and D. Bau III, **Numerical Linear | |
| Algebra**, SIAM, 1997. | |
| .. [Triggs] B. Triggs, P. F. McLauchlan, R. I. Hartley, and | |
| A. W. Fitzgibbon, **Bundle Adjustment -- A Modern Synthesis**, | |
| *Vision Algorithms: Theory and Practice*, pp. 298--372, 1999. | |
| .. [Weber] S. Weber, N. Demmel, T. C. Chan, and D. Cremers, **Power | |
| Bundle Adjustment for Large-Scale 3D Reconstruction**, *Proceedings | |
| of the IEEE/CVF Conference on Computer Vision and Pattern | |
| Recognition*, 2023. | |
| .. [Wiberg] T. Wiberg, **Computation of Principal Components When Data | |
| Are Missing**, *Proceedings of the Second Symposium of Computational | |
| Statistics*, pp. 229--236, 1976. | |
| .. [WrightHolt] S. J. Wright and J. N. Holt, **An Inexact Levenberg | |
| Marquardt Method for Large Sparse Nonlinear Least Squares**, | |
| *Journal of the Australian Mathematical Society Series B*, | |
| 26(4):387--403, 1985. | |
| .. [Zheng] Q. Zheng, Y. Xi, and Y. Saad, **A Power Schur Complement | |
| Low-Rank Correction Preconditioner for General Sparse Linear | |
| Systems**, *SIAM Journal on Matrix Analysis and Applications*, | |
| 42(2):659--682, 2021. |