TY - JOUR
T1 - A method of obtaining verified solutions for linear systems suited for Java
AU - Ozaki, K.
AU - Ogita, T.
AU - Miyajima, S.
AU - Oishi, S.
AU - Rump, S. M.
N1 - Funding Information:
This research was partially supported by CREST program, Japan Science and Technology Agency (JST), 21st Century COE Program (Productive ICT Academia Program, Waseda University) and Grant-in-Aid for Young Scientists (B) (16700017, 2004–2006) from the Ministry of Education, Science, Sports and Culture of Japan.
PY - 2007/2/15
Y1 - 2007/2/15
N2 - 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.
AB - 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.
KW - Java
KW - Linear system
KW - Verified computation
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U2 - 10.1016/j.cam.2005.08.034
DO - 10.1016/j.cam.2005.08.034
M3 - Article
AN - SCOPUS:33749679665
SN - 0377-0427
VL - 199
SP - 337
EP - 344
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -