  We analyze the convergence of quasi-Newton methods in exact and finite
precision arithmetic. In particular, we derive an upper bound for the
stagnation level and we show that any sufficiently exact quasi-Newton method
will converge quadratically until stagnation. In the absence of sufficient
accuracy, we are likely to retain rapid linear convergence. We confirm our
analysis by computing square roots and solving bond constraint equations in the
context of molecular dynamics. We briefly discuss implications for parallel
solvers.
