On a non-archimedean broyden method

Xavier Dahan, Tristan Vaccon

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトルISSAC 2020 - Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation
編集者Angelos Mantzaflaris
出版社Association for Computing Machinery
ページ114-121
ページ数8
ISBN(電子版)9781450371001
DOI
出版ステータスPublished - 2020 7 20
イベント45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020 - Kalamata, Virtual, Greece
継続期間: 2020 7 202020 7 23

出版物シリーズ

名前Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Conference

Conference45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020
国/地域Greece
CityKalamata, Virtual
Period20/7/2020/7/23

ASJC Scopus subject areas

  • 数学 (全般)

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