Convergence analysis of adaptive DIIS algorithms with application to electronic ground state calculations

This paper deals with a general class of algorithms for the solution fixed-point problems that we refer to as Anderson–Pulay acceleration . family includes DIIS technique and its variant sometimes called commutator-DIIS, both introduced by Pulay in 1980s accelerate convergence self-consistent field procedures quantum chemistry, well related Anderson which dates back 1960s, wealth techniques they have inspired. Such methods aim at accelerating any iteration method combining several iterates order generate next one each step. extrapolation process is characterised depth , i.e. number previous stored, crucial parameter efficiency method. It generally fixed an empirical value. In present work, consider two parameter-driven mechanisms let vary along iterations. first one, grows until certain nondegeneracy condition no longer satisfied; then stored (save last one) are discarded ``restarts’’. second adapt continuously eliminating step some oldest, less relevant, iterates. abstract setting, prove under natural assumptions local these adaptive methods, show can theoretically achieve superlinear rate them. We investigate their behaviour chemistry calculations. These numerical experiments variants exhibit faster than standard fixed-depth scheme, require on average computational effort per iteration. study complemented review known facts DIIS, particular link multisecant-type quasi-Newton methods.