Abstract
This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.
| Original language | English |
|---|---|
| Pages (from-to) | 229-239 |
| Number of pages | 11 |
| Journal | Reliable Computing |
| Volume | 9 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2003 Jun |
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ASJC Scopus subject areas
- Software
- Safety, Risk, Reliability and Quality
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Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations. / Ogita, Takeshi; Oishi, Shinichi; Ushiro, Yasunori.
In: Reliable Computing, Vol. 9, No. 3, 06.2003, p. 229-239.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations
AU - Ogita, Takeshi
AU - Oishi, Shinichi
AU - Ushiro, Yasunori
PY - 2003/6
Y1 - 2003/6
N2 - This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.
AB - This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.
UR - http://www.scopus.com/inward/record.url?scp=0038174786&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0038174786&partnerID=8YFLogxK
U2 - 10.1023/A:1024655416554
DO - 10.1023/A:1024655416554
M3 - Article
VL - 9
SP - 229
EP - 239
JO - Reliable Computing
JF - Reliable Computing
SN - 1385-3139
IS - 3
ER -