| Title: |
Computing the Matrix Logarithm with the Romberg Integration Method |
| Authors: |
Javier Ibáñez; José M. Alonso; Emilio Defez; Pedro Alonso-Jordá; Jorge Sastre |
| Source: |
Algorithms, Vol 16, Iss 9, p 434 (2023) |
| Publisher Information: |
MDPI AG, 2023. |
| Publication Year: |
2023 |
| Collection: |
LCC:Industrial engineering. Management engineering; LCC:Electronic computers. Computer science |
| Subject Terms: |
Romberg integration method; matrix logarithm; matrix functions; Industrial engineering. Management engineering; T55.4-60.8; Electronic computers. Computer science; QA75.5-76.95 |
| Description: |
The matrix logarithm function has applicability in many engineering and science fields. Improvements in its calculation, from the point of view of both accuracy and/or execution time, have a direct impact on these disciplines. This paper describes a new numerical algorithm devoted to matrix logarithm computation and using the Romberg integration method, together with the inverse scaling and squaring technique. This novel method was implemented and compared with three different state-of-the-art codes, all based on Padé approximation. The experimental results, under a heterogeneous matrix test battery, showed that the new method was numerically stable, with an elapsed time midway among the other codes, and it generally offered a higher accuracy. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
1999-4893 |
| Relation: |
https://www.mdpi.com/1999-4893/16/9/434; https://doaj.org/toc/1999-4893 |
| DOI: |
10.3390/a16090434 |
| Access URL: |
https://doaj.org/article/d84d00424d6d4d6e96552ce2bd36330c |
| Accession Number: |
edsdoj.84d00424d6d4d6e96552ce2bd36330c |
| Database: |
Directory of Open Access Journals |