# 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¶

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.

A. Bjorck, **Numerical Methods for Least Squares
Problems**, SIAM, 1996

D. C. Brown, **A solution to the general problem of
multiple station analytical stereo triangulation**, Technical
Report 43, Patrick Airforce Base, Florida, 1958.

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.

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.

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.

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

Timothy A. Davis, **Direct methods for Sparse Linear
Systems**, *SIAM*, 2006.

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.

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.

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.

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

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.

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.

R. G. Keys, **Cubic convolution interpolation for digital
image processing**, *IEEE Trans. on Acoustics, Speech, and Signal
Processing*, 29(6), 1981.

A. Kushal and S. Agarwal, **Visibility based
preconditioning for bundle adjustment**, *In Proceedings of the
IEEE Conference on Computer Vision and Pattern Recognition*, 2012.

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.

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

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.

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

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

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

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

T.P.A. Mathew, **Domain decomposition methods for the
numerical solution of partial differential equations**, Springer
Verlag, 2008.

S.G. Nash and A. Sofer, **Assessing a search direction
within a truncated newton method**, *Operations Research Letters*,
9(4):219-221, 1990.

J. Nocedal, **Updating Quasi-Newton Matrices with Limited
Storage**, *Mathematics of Computation*, 35(151): 773–782, 1980.

J. Nocedal and S. Wright, **Numerical Optimization**,
Springer, 2004.

S. S. Oren, **Self-scaling Variable Metric (SSVM) Algorithms
Part II: Implementation and Experiments**, Management Science,
20(5), 863-874, 1974.

W. H. Press, S. A. Teukolsky, W. T. Vetterling
and B. P. Flannery, **Numerical Recipes**, Cambridge University
Press, 2007.

C. J. F. Ridders, **Accurate computation of F’(x) and
F’(x) F”(x)**, Advances in Engineering Software 4(2), 75-76, 1978.

A. Ruhe and P.Å. Wedin, **Algorithms for separable
nonlinear least squares problems**, Siam Review, 22(3):318-337,
1980.

Y. Saad, **Iterative methods for sparse linear
systems**, SIAM, 2003.

I. Simon, N. Snavely and S. M. Seitz, **Scene Summarization
for Online Image Collections**, *International Conference on
Computer Vision*, 2007.

S. M. Stigler, **Gauss and the invention of least
squares**, *The Annals of Statistics*, 9(3):465-474, 1981.

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

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

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.

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.

T. Wiberg, **Computation of principal components when data
are missing**, In Proc. *Second Symp. Computational Statistics*,
pages 229-236, 1976.

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.

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.