My general concern is regarding denominator computation in this part $$\frac{s_ks_k^T}{y_k^Ts_k}\tag{1}$$ of the Hessian update in the method's algorithm/formula.
Formula has taken from here :
$$H_{k+1} = H_{k}- \frac{s_ks_k^T}{y_k^Ts_k}\tag{1} + \frac{H_{k}y_{k}y_{k}^TH_{k}}{y_k^TH_{k}y_{k}} $$
So, there definitely denominator will be a matrix. To calculate the equation, there is a need to find the inverse of all division, and, obviously saying, find the inverse of the denominator matrix.
Are there any ways to avoid calculating the inverse matrix? Or maybe there is some way to approximate the inverse matrix in this case?
Because of brute force matrix inversion approach is not working at all, because of computational issues.
I have seen one C++ implementation where we calculating this dividend as the inner product of 2 vectors. And I think that is not correct at all.
What I am missing?
Thanks in advance!