Static and Dynamic Response in O(N)

Wednesday, August 1, 2007 - 11:30am - 12:00pm
EE/CS 3-180
Matt Challacombe (Los Alamos National Laboratory)
Quantum locality leads to matrix sparsity, which may be exploited to achieve
an O(N) complexity through the use of an inexact, sparse linear algebra and
iterative methods. The framework for static response is developed around perturbation
of the spectral projector. In the case of dynamic response, an orbital free,
Rayleigh Quotient Iteration (RQI) like method is outlined. Problems with error accumulation,
associated with the inexact sparse linear algebra, are discussed and it is pointed out that
in the static case, the accumulation of errors on iteration quench as idempotence is reached.
In the dynamic case, it is shown that the frequencies are variational with respect to matrix
perturbation (truncation).