Abstract
We derive an estimate of the statistical error in calculating the trace of a large matrix by using random vectors, and show that the 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.
- Received 4 January 2004
DOI:https://doi.org/10.1103/PhysRevE.69.057701
©2004 American Physical Society