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Geometric Algebra Levenberg-Marquardt

Part of the Lecture Notes in Computer Science book series (LNIP,volume 11542)

Abstract

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.

Keywords

  • Geometric Algebra
  • Levenberg-Marquardt
  • Automatic differentiation
  • Non-linear estimation

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  • DOI: 10.1007/978-3-030-22514-8_51
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Acknowledgment

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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Correspondence to Steven De Keninck .

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De Keninck, S., Dorst, L. (2019). Geometric Algebra Levenberg-Marquardt. In: Gavrilova, M., Chang, J., Thalmann, N., Hitzer, E., Ishikawa, H. (eds) Advances in Computer Graphics. CGI 2019. Lecture Notes in Computer Science(), vol 11542. Springer, Cham. https://doi.org/10.1007/978-3-030-22514-8_51

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  • DOI: https://doi.org/10.1007/978-3-030-22514-8_51

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