| .. _sec-bibliography: | 
 |  | 
 | ============ | 
 | 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. | 
 |  | 
 | .. [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, | 
 |    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 & 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, | 
 |    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 & 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. |