We analyze various iteration procedures in many dimensions inspired by the SCF iteration used in first principles electronic structure calculations. We show that the simple mixing of densities can turn a divergent (or slowly convergent) iteration into a (faster) convergent process provided all the eigenvalues of the Jacobian are real and less than one. The problem of determining good mixing parameters are solved with the DIIS method of Pulay. We show that the large condition numbers often encountered in the linear system has no detrimental effect on the solution, i.e., the weights. Large weights can occur if the residual vectors are (nearly) linearly dependent. We show how to remove this linear dependence using the singular value decomposition (SVD).
A I P Conference Proceedings Series, 2009, p. 468-472