Random phase vector for calculating the trace of a large matrix

Details Random phase vector for calculating the trace of a large matrix Random phase vector for calculating the trace of a large matrix

2004-01-13

arxiv.org/abs/cond-mat/0401202v2

Phys. Rev. E 69, 057701 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, RevTex, Further description of real random vectors and self-averaging are added

Scientific paper

10.1103/PhysRevE.69.057701

We derive an estimate of statistical error in calculating the trace of a
large matrix by using random vector, and show that {\em random phase vector}
gives the results with the smallest statistical error for a given basis set.
This result supports use of random phase vectors in the calculation of density
of states and linear response functions of large quantum systems.

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