Correction to Partial Fraction Decomposition Coefficients for Chebyshev Rational Approximation on the Negative Real Axis

Abstract: Chebyshev rational approximation can be a viable method to compute the exponential of matrices with eigenvalues in the vicinity of the negative real axis, and it was recently applied successfully to solving nuclear fuel burnup equations. Determining the partial fraction decomposition (PFD) coefficients of this approximation can be difficult and they have been provided (for approximation orders 10 and 14) by Gallopoulos and Saad in "Efficient solution of parabolic equations by Krylov approximation methods", SIAM J. Sci. Stat. Comput., 13(1992). It was recently discovered that the order 14 coefficients contain errors and result in 100 times poorer accuracy than expected by theory. The purpose of this note is to provide the correct PFD coefficients for approximation orders 14 and 16 and to briefly discuss the approximation accuracy resulting from the erroneous coefficients.