Singular value decomposition of energy matrices in theoretical atomic structure calculations
作者:
Gilles Verbockhaven,
JØrgen E. Hansen,
期刊:
Molecular Physics
(Taylor Available online 2000)
卷期:
Volume 98,
issue 16
页码: 1117-1123
ISSN:0026-8976
年代: 2000
DOI:10.1080/00268970050080483
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The singular value decomposition, SVD, is applied to the linear eigenvalue problem in atomic structure calculations. By comparing with recent calculations of energy levels in neutral Ca, it is shown that the SVD can give quite accurate results and much faster than normal diagonalization techniques, even of the Davidson type. However, the energy levels calculated in this approach are more strongly bound than the real eigenvalues, and this is ascribed to an artefact of the SVD, caused by the use of a discretized continuum in the calculations. This effect can lead to fairly large errors if there is strong CI present. The property of the linear eigenvalue problem that the spectrum is unchanged when a constant is added to the diagonal does not apply to the SVD. This means that it is impossible to solve the problems connected with a discretized continuum simply by shifting the spectrum.
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