Fast and parallel interval arithmetic

Publikationstyp
Journal Article
Publikationsdatum
1999-09
Sprache
English
Author
Rump, Siegfried M. orcid-logo
Institut
Zuverlässiges Rechnen E-19 
TORE-URI
http://hdl.handle.net/11420/9361
Enthalten in
BIT 
Volume
39
Issue
3
Start Page
534
End Page
554
Citation
BIT Numerical Mathematics 39 (3): 534-554 (1999-09)
Publisher DOI
10.1023/A:1022374804152
Scopus ID
2-s2.0-0042043158
Publisher
Swets & Zeitlinger
Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Moreover, we describe an implementation of midpoint-radius interval arithmetic entirely using BLAS. Therefore, in particular, matrix operations are very fast on almost any computer, with minimal effort for the implementation. Especially, with the new definition it is seemingly the first time that full advantage can be taken of the speed of vector and parallel architectures. The algorithms have been implemented in the Matlab interval toolbox INTLAB.
Schlagworte
BLAS
Infimum-supremum
Interval arithmetic
Midpoint-radius
Parallel computer
DDC Class
004: Informatik
510: Mathematik