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Random phase vector for calculating the trace of a large matrix

Toshiaki Iitaka·Toshikazu Ebisuzaki
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Abstract

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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Toshiaki Iitaka, Toshikazu Ebisuzaki. 2004-02-05. Random phase vector for calculating the trace of a large matrix. https://doi.org/10.1103/physreve.69.057701

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