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.. _sec-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.
.. [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.
.. [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 & 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.
.. [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,
.. [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 & 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
& 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,
.. [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 & 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 &
A. W. Fitzgibbon, **Bundle Adjustment: A Modern Synthesis**,
Proceedings of the International Workshop on Vision Algorithms:
Theory and Practice, pp. 298-372, 1999.
.. [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.