  Density functional theory calculations use a significant fraction of current
supercomputing time. The resources required scale with the problem size,
internal workings of the code and the number of iterations to convergence, the
latter being controlled by what is called mixing. This note describes a new
approach to handling trust-regions within these and other fixed-point problems.
Rather than adjusting the trust-region based upon improvement, the prior steps
are used to estimate what the parameters and trust-regions should be,
effectively estimating the optimal Polyak step from the prior history. Detailed
results are shown for eight structures using both the Good and Bad Multisecant
versions as well as Anderson and a hybrid approach, all with the same
predictive method. Additional comparisons are made for thirty-six cases with
fixed algorithm Greed The predictive method works well independent of which
method is used for the candidate step, and is capable of adapting to different
problem types particularly when coupled with the hybrid approach. It would be
premature to claim that it is the best possible approach, but the results
suggest that it may be.
