Verification methods for linear systems using ufp estimation with rounding-to-nearest-Reference-Cited by-同舟云学术

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

Published:2013 Issue:1 Volume:4 Page:12-22
ISSN:2185-4106
Container-title:Nonlinear Theory and Its Applications, IEICE
language:en
Short-container-title:NOLTA

Author:

Morikura Yusuke¹,Ozaki Katsuhisa²³,Oishi Shin'ichi⁴³

Affiliation:

1. Graduate School of Fundamental Science and Engineering, Waseda University

2. Department of Mathematical Sciences, Shibaura Institute of Technology

3. CREST, Japan Science and Technology Agency, Japan

4. Faculty of Science and Engineering, Waseda University

Publisher

Institute of Electronics, Information and Communications Engineers (IEICE)

Subject

Rehabilitation,Physical Therapy, Sports Therapy and Rehabilitation,General Medicine

Link

https://www.jstage.jst.go.jp/article/nolta/4/1/4_12/_pdf

Reference13 articles.

1. [1] S. Oishi and S.M. Rump, “Fast verification of solutions of matrix equations,” Numer. Math., vol. 90, no. 4, pp. 755-773, February 2002.

2. [2] T. Ogita, S.M. Rump, and S. Oishi, “Verified solutions of linear systems without directed rounding,” Technical Report 2005-04, Advanced Research Institute for Science and Engineering, Waseda University, Tokyo, Japan, July 2005.

3. [3] K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump, “A method of obtaining verified solutions for linear systems suited for Java,” Journal of Computational and Applied Mathematics, vol. 199, no. 2, pp. 337-344, February 2007.

4. [4] T. Ogita, S. Oishi, and Y. Ushiro, “Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations,” Reliable Computing, vol. 9, no. 3, pp. 229-239, June 2003.

5. [5] T. Ohta, T. Ogita, S.M. Rump, and S. Oishi, “Numerical method for dense linear systems with Arbitrarily Ill-conditioned Matrices,” Transactions of the Japan Society for Industrial and Applied Mathematics, vol. 15, no. 3, pp. 269-286, September 2005.

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