Random phase vector for calculating the trace of a large matrix.
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.
Iitaka
Toshiaki
T
Ebisuzaki Computational Astrophysics Laboratory, RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan. tiitaka@riken.jp
Ebisuzaki
Toshikazu
T