Geometric Algebra Levenberg-Marquardt

  • Steven De KeninckEmail author
  • Leo Dorst
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11542)


This paper introduces a novel and matrix-free implementation of the widely used Levenberg-Marquardt algorithm, in the language of Geometric Algebra. The resulting algorithm is shown to be compact, geometrically intuitive, numerically stable and well suited for efficient GPU implementation. An implementation of the algorithm and the examples in this paper are publicly available.


Geometric Algebra Levenberg-Marquardt Automatic differentiation Non-linear estimation 



The authors would like to thank Charles Gunn for his valuable feedback on, and Hugo Hadfield and Vincent Nozick for their proofreading of an early version of this article.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Matrix FactoryHingeneBelgium
  2. 2.University of AmsterdamAmsterdamThe Netherlands

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