Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications
2012
Session Number:D2L-D
Session:
Number:877
Memory Reduced Implementation of Error-Free Transformation of Matrix Multiplication and its Performance
Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi Oishi,
pp.877-880
Publication Date:
Online ISSN:2188-5079
[1] ANSI: IEEE Standard for Floating-Point Arithmetic, Std 754-2008, 2008.
[2] T. Ogita, S. M. Rump, S. Oishi: Accurate sum and dot product, SIAM J. Sci. Comput., 26, 1955-1988 (2005).
[3] S. M. Rump, T. Ogita, S. Oishi: Accurate Floating-Point Summation Part I: Faithful Rounding, SIAM J. Sci. Comput., 31:1, 189-224 (2008).
[4] S. M. Rump, T. Ogita, S. Oishi: Accurate Floating-Point Summation Part II: Sign, K-fold Faithful and Rounding to Nearest, SIAM J. Sci. Comput., 31:2, 1269-1302 (2008).
[5] K. Ozaki, T. Ogita, S. Oishi, S. M. Rump: Error-Free Transformation ofMatrixMultiplication by Using Fast Routines of Matrix Multiplication and its Applications, Numerical Algorithms, 59:1, pp. 95-118 (2012).
[6] The MPFR Library: http://www.mpfr.org/
[7] exflib-extend precision floating-point arithmetic library: http://www-an.acs.i.kyoto-u.ac.jp/fujiwara/exflib/exflib-index.html