A Comparative Study on Methods for Convergence Acceleration of Iterative Vector Sequences

✍ Scribed by V. Eyert

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 396 KB
• Volume: 124
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0059

✦ Synopsis

We discuss several methods for accelerating the convergence of the iterative solution of nonlinear equation systems commonly in tion they are solved by iteration (for a more detailed deuse and point to interrelations between them. In particular we invesscription see Ref.

[9] and references therein).

tigate two of the most sophisticated schemes, namely the Anderson Usually each of these iterations itself needs a lot of CPU mixing and the Broyden update, both generalized to the considertime and thus reducing their number by accelerating the ation of arbitrarily many previous iterations. For the Broyden convergence would save computer resources or else allow method we give a new derivation which is much simpler than that for larger systems to be investigated [10]. As concerns recently proposed by Vanderbilt and Louie. We show that if the additional parameters invented by these authors in order to increase these general demands, we believe electronic structure calflexibility are used to optimize the convergence of the iteration culations are no exception.

process they in fact cancel out. In addition we prove that in this

In order to get a better feeling of which method would (optimal) case the Anderson mixing and the Broyden update as be best suited to the context just outlined we started the applied to the inverse Jacobian are fully identical. Thus we come present analysis of convergence acceleration schemes.

to the conclusion that neither of these schemes is superior. Moreover, we show that Broyden update of the inverse Jacobian is supe-Here we concentrated especially on quasi-Newtonrior to updating the Jacobian itself. Finally we propose an extension Raphson schemes and generalized secant methods. When of the Anderson mixing which avoids the numerical difficulties all applying the former class to nonlinear equation systems these methods are faced with.