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Error vector choice in direct inversion in the iterative subspace method
Author(s) -
Ionova Irina V.,
Carter Emily A.
Publication year - 1996
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/(sici)1096-987x(199612)17:16<1836::aid-jcc4>3.0.co;2-o
Subject(s) - subspace topology , inversion (geology) , computer science , convergence (economics) , algorithm , iterative method , mathematics , mathematical optimization , artificial intelligence , paleontology , structural basin , economics , biology , economic growth
Based on Banach's principle, we formally obtain possible choices for an error vector in the direct inversion in the iterative subspace (DIIS) method. These choices not only include all previously proposed error vectors, but also a new type of error vector which is computationally efficient and applicable to much wider range of problems. The error vector analysis also reveals a strong connection between DIIS and damping, thus adding to understanding of the reasons behind DIIS's effect on convergence. We illustrate our conclusions with several examples. © 1996 by John Wiley & Sons, Inc.