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Search for stationary points of arbitrary index by augmented Hessian method
Author(s) -
Khait Yu. G.,
Panin A. I.,
Averyanov A. S.
Publication year - 1995
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560540602
Subject(s) - hessian matrix , stationary point , eigenvalues and eigenvectors , mathematics , correctness , convergence (economics) , current (fluid) , simple (philosophy) , hessian equation , point (geometry) , bottleneck , mathematical analysis , mathematical optimization , computer science , algorithm , geometry , physics , differential equation , philosophy , epistemology , quantum mechanics , first order partial differential equation , embedded system , economics , thermodynamics , economic growth
Convergence properties of the augmented Hessian ( AH ) method when searching for stationary points of an arbitrary fixed index are investigated. It is shown that the displacement vector of this method is proportional to one of the Hessian eigenvectors if the current point is far from a stationary one of the required index. A simple and reliable criterion for nearness of the current point to a stationary one of the desired index is proposed. The efficiency of a new one‐dimensional optimization scheme that uses this criterion is studied. The case of coincidence of Hessian eigenvalues, which is a bottleneck of the standard AH method, is analyzed. A relation of the AH method to those by Poppinger and Wales is outlined. The correctness of the results obtained is illustrated on an example of a model surface. © 1995 John Wiley & Sons, Inc.