On a non-archimedean broyden method

Xavier Dahan, Tristan Vaccon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Newton's method is an ubiquitous tool to solve equations, both in the archimedean and non-archimedean settings - - for which it does not really differ. Broyden was the instigator of what is called "quasi-Newton methods". These methods use an iteration step where one does not need to compute a complete Jacobian matrix nor its inverse. We provide an adaptation of Broyden's method in a general non-archimedean setting, compatible with the lack of inner product, and study its Q and R convergence. We prove that our adapted method converges at least Q-linearly and R-superlinearly with R-order [EQUATION] in dimension m. Numerical data are provided.

Original languageEnglish
Title of host publicationISSAC 2020 - Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation
EditorsAngelos Mantzaflaris
PublisherAssociation for Computing Machinery
Pages114-121
Number of pages8
ISBN (Electronic)9781450371001
DOIs
Publication statusPublished - 2020 Jul 20
Externally publishedYes
Event45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020 - Kalamata, Virtual, Greece
Duration: 2020 Jul 202020 Jul 23

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Conference

Conference45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020
Country/TerritoryGreece
CityKalamata, Virtual
Period20/7/2020/7/23

Keywords

  • broyden's method
  • p-adic algorithm
  • p-adic approximation
  • power series
  • quasi-newton
  • symbolic-numeric
  • system of equations

ASJC Scopus subject areas

  • Mathematics(all)

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