Fast spectral projection algorithms for density-matrix computations

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. (C) 1999 Academic Press.