Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:D2L-D

Session:

Number:881

Verified bounds for Least Squares Problems and Underdetermined Linear Systems

Siegfried M. Rump,  

pp.881-882

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.881

PDF download (281.9KB)

Summary:

References:

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[2] S. Graillat. Applications of fast and accurate summation in computational geometry. In Proceedings of the 2006 ACM Symposium on Applied Computing, number CMS-108, 2006.

[3] D.E. Knuth. The Art of Computer Programming-Seminumerical Algorithms, Vol. 2, Addison Wesley, Reading, Massachusetts, 1969.

[4] S. Miyajima. Fast enclosure for solutions in underdetermined systems. J. Comput. Appl. Math., 234:3436-3444, 2010.

[5] T. Ogita, S.M. Rump, and S. Oishi. Accurate sum and dot product. SIAM J. Sci. Comput., 26(6):1955-1988, 2005.

[6] S.M. Rump. INTLAB - Interval Laboratory, Version 6. http://www.ti3.tu-harburg.de/rump, 1998-2012.

[7] S.M. Rump. Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. SIAM J. Matrix Anal. Appl. (SIMAX), 33(1):130-148, 2012.

[8] S.M. Rump, T. Ogita, and S. Oishi. Accurate floating-point summation part I: Faithful rounding. SIAM J. Sci. Comput., 31(1):189-224, 2008.