1Blurb:: 2Use the Symmetric Rank 1 update method to compute quasi-Hessians 3Description:: 4The Symmetric Rank 1 (SR1) update (specified with the keyword \c sr1) 5will be used to compute quasi-Hessians. 6 7\f[ 8B_{k+1} = B_k + \frac{(y_k - B_k s_k)(y_k - B_k s_k)^T}{(y_k - B_k s_k)^T s_k} 9\f] 10 11where \f$B_k\f$ is the \f$k^{th}\f$ approximation to the Hessian, 12\f$s_k = x_{k+1} - x_k\f$ is the step and 13\f$y_k = \nabla f_{k+1} - \nabla f_k\f$ is the corresponding yield 14in the gradients. 15 16<b> Notes </b> 17 18\li Initial scaling of 19\f$\frac{y_k^T y_k}{y_k^T s_k} I\f$ is used for \f$B_0\f$ prior to the first 20update. 21\li Numerical safeguarding is used 22to protect against numerically small denominators within the updates. 23\li This safeguarding skips the update if 24\f$|(y_k - B_k s_k)^T s_k| < 10^{-6} ||s_k||_2 ||y_k - B_k s_k||_2\f$ 25 26Topics:: 27Examples:: 28Theory:: 29Faq:: 30See_Also:: 31