Reducing the truncation error in Taylor model multiplication

Publikationstyp
Journal Article
Date Issued
2024-01-06
Sprache
English
Author(s)
Bünger, Florian  
Mathematik E-10  
TORE-URI
https://hdl.handle.net/11420/45287
Journal
Numerical algorithms  
Volume
97
Issue
2
Start Page
819
End Page
841
Citation
Numerical Algorithms 97 (2): 819-841 (2024)
Publisher DOI
10.1007/s11075-023-01725-4
Scopus ID
2-s2.0-85181461404
Publisher
Springer
We present two new methods, a simple fast and a slower more precise one, to reduce the truncation error occurring during multiplication in verified Taylor model arithmetic. These methods were implemented in MATLAB in INTLAB’s Taylor model toolbox which targets solving ordinary differential equations rigorously, i.e., numerical solutions are computed along with rigorous error bounds that include all numerical as well as all rounding errors so that the exact solution must lie within these error bounds. The methods are applied to several test cases to show their effect.
Subjects
Initial value problems
Ordinary differential equations
Taylor models
DDC Class
510: Mathematics