@Article{escande:ima:2016,
  author    = {Escande, Adrien},
  title     = {Fast closest logarithm algorithm in the special orthogonal group},
  journal   = {IMA Journal of Numerical Analysis},
  year      = {2016},
  volume    = {36},
  number    = {2},
  pages     = {675--687},
  month     = {April},
  doi       = {https://doi.org/10.1093/imanum/drv027},
  url       = {https://raw.githubusercontent.com/aescande/website/master/papers/2016\_IMAJNA\_Escande.pdf},
  keywords  = {interpolation, special orthogonal group, logarithm},
  abstract  = {For interpolating between elements of SO(n)\nolinebreak , it is attractive to work in so(n)\nolinebreak , passing from one space to the other via the exponential map. However, the logarithm is a multi-valued map and the choice of a particular image affects the quality of the interpolation. In this paper, we propose a fast and accurate algorithm to compute the image that seems the most appropriate for interpolation: given Q in SO(n) and A in so(n)\nolinebreak , our algorithm returns the logarithm of Q which is the closest to A\nolinebreak , under minimal conditions on Q\nolinebreak . We carefully study the mathematical properties of our problem to establish the algorithm, discuss its implementation and demonstrate its efficiency.},
  publisher = {OXFORD UNIV PRESS},
  address   = {GREAT CLARENDON ST, OXFORD OX2 6DP, ENGLAND}
}