On a non-archimedean broyden method
Symbolic Computation
2020-09-04 v1 Numerical Analysis
Numerical Analysis
Number Theory
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 in dimension m. Numerical data are provided.
Cite
@article{arxiv.2009.01511,
title = {On a non-archimedean broyden method},
author = {Xavier Dahan and Tristan Vaccon},
journal= {arXiv preprint arXiv:2009.01511},
year = {2020}
}