Accurate and efficient matrix exponential computation

Abstract

This work gives a new formula for the forward relative error of matrix exponential Taylor approximation and proposes new bounds for it depending on the matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the matrix exponential. A Matlab version of the new algorithm is provided and compared with Padé state-of-the-art algorithms obtaining higher accuracy in the majority of tests at similar or even lower cost.

Keywords:

• matrix exponential
• scaling and squaring
• Taylor series
• error analysis

2010 AMS Subject Classifications:

• 65F30
• 65F35
• 65F60

Acknowledgements

This work has been supported by the Programa de Apoyo a la Investigación y el Desarrollo of the Universitat Politècnica de València grant PAID-06-11-2020