Polynomial approximations for the matrix logarithm with computation graphs
Numerical Analysis
2024-01-19 v1 Numerical Analysis
Abstract
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational effort lies in matrix-matrix multiplications and left matrix division. In this work we illustrate that the number of such operations can be substantially reduced, by using a graph based representation of an efficient polynomial evaluation scheme. A technique to analyze the rounding error is proposed, and backward error analysis is adapted. We provide substantial simulations illustrating competitiveness both in terms of computation time and rounding errors.
Cite
@article{arxiv.2401.10089,
title = {Polynomial approximations for the matrix logarithm with computation graphs},
author = {Elias Jarlebring and Jorge Sastre and J. Javier Ibáñez González},
journal= {arXiv preprint arXiv:2401.10089},
year = {2024}
}