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Fast Spectral Projection Algorithms for Density-Matrix Computations

✍ Scribed by Gregory Beylkin; Nicholas Coult; Martin J Mohlenkamp

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 196 KB
Volume: 152
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1999.6215

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✦ Synopsis

We present a fast algorithm for the construction of a spectral projector. This algorithm allows us to compute the density matrix, as used in, e.g., the Kohn-Sham iteration, and so obtain the electron density. We compute the spectral projector by constructing the matrix sign function through a simple polynomial recursion. We present several matrix representations for fast computation within this recursion, using bases with controlled space-spatial-frequency localization. In particular we consider wavelet and local cosine bases. Since spectral projectors appear in many contexts, we expect many additional applications of our approach.

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