2025/12/28 by Hen, Itay
#Computational Physics (physics.comp-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2512.23061
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically stable evaluation of high-order exponential divided differences for dynamically evolving node sets remains a significant computational challenge. We present a Chebyshev-polynomial-based algorithm that addresses this problem by combining the Chebyshev-Bessel expansion of the exponential function with a direct recurrence for Chebyshev divided differences. The method achieves a computational cost of \cal O(qN), where q is the divided-difference order and N is the Chebyshev truncation length. We show that N scales linearly with the spectral width through the decay of modified Bessel coefficients, while the dependence on q enters only through structural polynomial constraints. We further develop an incremental update scheme for dynamic node sets that enables the insertion or removal of a single node in \cal O(N) time when the affine mapping interval is held fixed. A full C++ reference implementation of the algorithms described in this work is publicly available.