  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
$2^{\frac{1}{2m}}$ in dimension m. Numerical data are provided.
