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The C 2 ‐DIIS convergence acceleration algorithm
Author(s) -
Sellers Harrell
Publication year - 1993
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.560450106
Subject(s) - computer science , iterated function , algorithm , convergence (economics) , mathematics , mathematical analysis , economics , economic growth
We present a theoretical and numerical comparison between two DIIS algorithms to which we refer herein as C 1 ‐ DIIS and C 2 ‐ DIIS . The C 2 ‐ DIIS algorithm is shown to be equivalent to the traditional C 1 ‐ DIIS algorithm near convergence and more stable numerically as regards the accumulation of round‐off error when the C 1 ‐ DIIS equations become (nearly) singular. The C 2 ‐ DIIS algorithm also offers alternative solutions to the DIIS equations when anharmonicities or numerical difficulties are problematic. These properties of the C 2 ‐ DIIS algorithm allow the use of much larger DIIS spaces, obviating the need for truncation of the DIIS space, which, when done, usually results in a loss of information contained in the iterated subspace. The C 2 ‐ DIIS method can be considered to be a variant of the singular value decomposition method. © 1993 John Wiley & Sons, Inc.