@inproceedings{3ee58c5620b344dbb2307fe90295111f,

title = "On a non-archimedean broyden method",

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.",

keywords = "broyden's method, p-adic algorithm, p-adic approximation, power series, quasi-newton, symbolic-numeric, system of equations",

author = "Xavier Dahan and Tristan Vaccon",

note = "Publisher Copyright: {\textcopyright} 2020 ACM.; 45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020 ; Conference date: 20-07-2020 Through 23-07-2020",

year = "2020",

month = jul,

day = "20",

doi = "10.1145/3373207.3404045",

language = "English",

series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",

publisher = "Association for Computing Machinery",

pages = "114--121",

editor = "Angelos Mantzaflaris",

booktitle = "ISSAC 2020 - Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation",

}