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
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
CountryGreece
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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