Some comments on the DIIS method
Ron L. Shepard, Michael Minkoff · Molecular Physics · 2007
Over twenty ways to solve the DIIS equation are introduced and discussed. Some of these solution methods are inherently inaccurate and are never recommended, others have some efficiency or accuracy advantages that may be exploited in different situations. Two of these ways, linear least squares with substitution and elimination, and linear least squares with equality constraint, have the potential to produce solutions that are significantly more accurate than the traditional normal equation solutions. The choice of the most accurate solution approach for a given problem depends on various vector and matrix norm relations which are discussed. The advantage of one of these methods is demonstrated on a model problem, which has a closed-form solution. A simple geometrical interpretation is given for the DIIS method that involves minimization of a function value within a particular multidimensional plane.