# Bibliography

## Background Reading

For a short but informative introduction to the subject 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 coverage 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]

A. Bjorck, 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 Airforce Base, Florida, 1958.

[ByrdNocedal]

R. H. Byrd, J. Nocedal, R. B. Schanbel, Representations of Quasi-Newton Matrices and their use in Limited Memory Methods, Mathematical Programming 63(4):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, TOMS, 35(3), 2008.

[Conn]

A.R. Conn, N.I.M. Gould, and P.L. Toint, Trust region methods, Society for Industrial Mathematics, 2000.

[Davis]

Timothy 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, 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 Trans. Math. Softw., 43(4), 2017.

[HartleyZisserman]

R.I. Hartley and A. Zisserman, Multiview Geometry in Computer Vision, Cambridge University Press, 2004.

[Hertzberg]

C. Hertzberg, R. Wagner, U. Frese and L. Schroder, 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 Trans. on Acoustics, Speech, and Signal Processing, 29(6), 1981.

[KushalAgarwal]

A. Kushal and S. Agarwal, Visibility based preconditioning for bundle adjustment, In 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, 177(2):375-397, 2005.

[Levenberg]

K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math, 2(2):164-168, 1944.

[LiSaad]

Na 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, 2007.

[LourakisArgyros]

M. L. A. Lourakis, A. A. Argyros, Is Levenberg-Marquardt the most efficient algorithm for implementing bundle adjustment?, International Conference on Computer Vision, 2005.

[Madsen]

K. Madsen, H.B. Nielsen, and O. Tingleff, Methods for nonlinear least squares problems, 2004.

[Mandel]

J. Mandel, On block diagonal and Schur complement preconditioning, Numer. Math., 58(1):79-93, 1990.

[Marquardt]

D.W. Marquardt, An algorithm for least squares estimation of nonlinear parameters, J. SIAM, 11(2):431-441, 1963.

[Mathew]

T.P.A. Mathew, Domain decomposition methods for the numerical solution of partial differential equations, Springer Verlag, 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. Wright, Numerical Optimization, Springer, 2004.

[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, 1978.

[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, 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. Tenenbaum and B. Director, How Gauss Determined the Orbit of Ceres.

[TrefethenBau]

L.N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.

[Triggs]

B. Triggs, P. F. Mclauchlan, R. I. Hartley and A. W. Fitzgibbon, Bundle Adjustment: A Modern Synthesis, Proceedings of the International Workshop on Vision Algorithms: Theory and Practice, pp. 298-372, 1999.

[Weber]

S. Weber, N. Demmel, TC Chan, D. Cremers, Power Bundle Adjustment for Large-Scale 3D Reconstruction, IEEE Conference on Computer Vision and Pattern Recognition, 2023.

[Wiberg]

T. Wiberg, Computation of principal components when data are missing, In Proc. Second Symp. Computational Statistics, pages 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, 2021.