Verification methods for linear systems using ufp estimation with rounding-to-nearest

被引：3

作者：

Morikura, Yusuke ^{[1
]}

Ozaki, Katsuhisa ^{[2
,4
]}

Oishi, Shin'ichi ^{[3
,4
]}

机构：

[1] Waseda Univ, Grad Sch Fundamental Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan

[2] Shibaura Inst Technol, Dept Math Sci, Minuma Ku, Saitama, Saitama 3378570, Japan

[3] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan

[4] Japan Sci & Technol Agcy, CREST, Tokyo, Japan

来源：

IEICE NONLINEAR THEORY AND ITS APPLICATIONS | 2013年 / 4卷 / 01期

基金：

日本科学技术振兴机构;

关键词：

linear systems; verified numerical computation;

D O I：

10.1587/nolta.4.12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：12 / 22

页数：11

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