BFGS update formula

$$H_{k+1}=H_k+\frac{s_k{s}_k^T}{s_k^T{y}_k}-\frac{H_k{y}_k{y}_k^T{H}_k}{y_k^T{H}_k{y}_k}$$

Where

$$\begin{array}{rlr}{s}_k& ={\theta }_{k+1}-{\theta }_k& \text{The step taken}\\ y& =\nabla E({\theta }_{k+1})-\nabla E({\theta }_k)& \text{The difference in gradients}\\ H_k& & \text{The current approximation to the inverse Hessian matrix}\end{array}$$