On the computation of the matrix function in the von Neumann entropy with the double exponential formula

抄録

This letter considers the double exponential (DE) formula for computing the matrix function –Alog(A), where A is a Hermitian positive semidefinite matrix and tr(A) = 1. The motivation of this work is to utilize the DE formula without selecting parameters. In order to accomplish this, we present a method for truncating the infinite interval transformed by the DE transformation based on an error analysis to achieve the required accuracy. We also discuss techniques to select the number of abscissas. In addition, we report that an appropriate choice of a parameter in the DE transformation will improve the convergence.