Efficient scaling and squaring method for the matrix exponential

Autor:	Blanes, Sergio, Kopylov, Nikita, Seydaoğlu, Muaz
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis 15A16 G.1.3 G.1.7
Druh dokumentu:	Working Paper
Popis:	This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then exp(A) belongs to its associated Lie group, being a property which is preserved by diagonal Pad\'e approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations. Comment: 26 pages, 4 figures, 3 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.12789 Zobrazit plný text záznamu View this record from Arxiv