A method of obtaining verified solutions for linear systems suited for Java

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2007-02, Vol.199 (2), p.337-344
Main Authors: Ozaki, K., Ogita, T., Miyajima, S., Oishi, S., Rump, S.M.
Format: Article
Language:English
Subjects:
Algebra
Applied sciences
Computer science
control theory
systems
Exact sciences and technology
Java
Linear and multilinear algebra, matrix theory
Linear system
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Programming languages
Sciences and techniques of general use
Software
Verified computation
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.08.034