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A method of obtaining verified solutions for linear systems suited for Java
Publikationstyp
Journal Article
Date Issued
2006-01-19
Sprache
English
Institut
TORE-URI
Volume
199
Issue
2
Start Page
337
End Page
344
Citation
Journal of Computational and Applied Mathematics 199 (2): 337-344 (2007)
Publisher DOI
Scopus ID
Publisher
North-Holland, Elsevier Science
Recent development of Java's optimization techniques makes Java one of the most useful programming languages for numerical computations. This paper proposes a numerical method of obtaining verified approximate solutions of linear systems. Usual methods for verified computations use switches of rounding modes defined in IEEE standard 754. However, such switches of rounding modes have not been supported in Java. This method avoids using directed rounding, so that it is implementable on a wide range of programming languages including Java. Numerical experiments using Java illustrate that the method can give a very accurate error bound for an approximate solution of a linear system with almost same computational cost as that for calculating an approximate inverse by the Gaussian elimination.
Subjects
Java
Linear system
Verified computation
DDC Class
004: Informatik
510: Mathematik