Talk:Broyden's method

untitled
This method sucks, the jacobian is way wrong after updating. Is it because my step size is too large?

best wishes, 150.135.211.246 (talk) 23:22, 12 September 2014 (UTC)

It is not suppose to be a perfect update. It is estimating the nonlinearity in only 1 direction. If you have strong nonlinearity you may only get an advantage for a couple updates. So the approximate updates you get from Broyden's method should be mixed in with full Jacobian updates. The relative mix is problem dependent. For my work around 4-5 broyden updates between each full Jacobian update. You can use rate of improvement to judge this. — Preceding unsigned comment added by 2001:878:200:1055:224:2CFF:FE6C:92B (talk) 10:53, 8 September 2016 (UTC)

Too expensive formula?
Formula
 * $$\mathbf J_n^{-1} = \mathbf J_{n - 1}^{-1} + \frac{\Delta \mathbf x_n - \mathbf J^{-1}_{n - 1} \Delta \mathbf f_n}{\Delta \mathbf x_n^{\mathrm T} \mathbf J^{-1}_{n - 1} \Delta \mathbf f_n} \Delta \mathbf x_n^{\mathrm T} \mathbf J^{-1}_{n - 1}$$

seems to be too expansive. But using associativity we don' must make all multiplication from left to right. And it is ok Borneq (talk) 14:05, 6 April 2018 (UTC)