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

Authors:
K. Ozaki;T. Ogita;S. Miyajima;S. Oishi;S. M. Rump
Affiliations:
Graduate School of Science and Engineering, Waseda University, Tokyo, Japan;CREST, Japan Science and Technology Agency (JST) and Faculty of Science and Engineering, Waseda University, Tokyo, Japan;Faculty of Science and Engineering, Waseda University, Tokyo, Japan;Faculty of Science and Engineering, Waseda University, Tokyo, Japan;Institut für Informatik III, Technische Universität Hamburg-Harburg, Hamburg, Germany
Venue:
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Year:
2007

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Abstract

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.