The Newton iteration on Lie groups

B. Owren, Bruno Welfert

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

We define the Newton iteration for solving the equation f(y) = 0, where f is a map from a Lie group to its corresponding Lie algebra. Two versions are presented, which are formulated independently of any metric on the Lie group. Both formulations reduce to the standard method in the Euclidean case, and are related to existing algorithms on certain Riemannian manifolds. In particular, we show that, under classical assumptions on f, the proposed method converges quadratically. We illustrate the techniques by solving a fixed-point problem arising from the numerical integration of a Lie-type initial value problem via implicit Euler.

Original languageEnglish (US)
Pages (from-to)121-145
Number of pages25
JournalBIT Numerical Mathematics
Volume40
Issue number1
DOIs
StatePublished - Mar 2000

Keywords

  • Geometric integration
  • Lie algebras
  • Lie groups
  • Newton iteration
  • Numerical methods on manifolds

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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