Retrieving "Quasi Newton Method" from the archives

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1. Numerical Methods In Chemistry

   Linked via "quasi-Newton methods"

   | Newton-Raphson (NR) | Quadratic | $O(N^3)$ | Requires inversion/factorization of the Hessian matrix $\mathbf{H}$ |
   The Newton-Raphson method , while fast, requires computation and inversion of the Hessian matrix , $\mathbf{H}{ij} = \frac{\partial^2 E}{\partial Ri \partial R_j}$. In systems larger than $N=50$ atoms, the $O(N^3)$ scaling becomes prohibitive, necessitating the use of quasi-Newton methods (e.g., [BFGS](/entries/bfgs-op…