Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special section on Recent Progress in Verified Numerical Computations
Verification methods for linear systems using ufp estimation with rounding-to-nearest
Yusuke MorikuraKatsuhisa OzakiShin'ichi Oishi
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2013 Volume 4 Issue 1 Pages 12-22


This paper is concerned with verification methods for numerical solutions of linear systems. Many methods for the verification require switches of rounding modes defined by the IEEE 754 standard. However, the switches cannot be supported in several computational environments. In such cases, Ogita-Rump-Oishi's method can work on such environments. Recently, Rump developed new error estimates of floating-point summation and dot product. The aim of this paper is to improve Ogita-Rump-Oishi's error estimates by using the error estimates by Rump. In addition, the computational cost of our method is comparable to that of Ogita-Rump-Oishi's method.

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© 2013 The Institute of Electronics, Information and Communication Engineers
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