The GDIIS algorithm

This method [75] uses simplex interpolation combined with an update step such as BFGS. The variational functional is 

The interpolated gradient vector is p = p a and the interpolated coordinate vector is q = J2k In the GDIIS algorithm, a currently updated estimate of the inverse Hessian is used to estimate a coordinate step based on these interpolated vectors. This gives 

In test calculations [75] this algorithm was found to produce rapid convergence. When combined with single-step (in = 1) BFGS update of the inverse Hessian, this is a very efficient algorithm. 

This algorithm, standard in the widely used GAUSSIAN program system, is a rank-m update of the Hessian matrix, in an orthonormal basis [356], A basis of unit vectors is constructed in the m -dimensional vector space spanned by the increments Aq. For k = 1, m, define 

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