Summary

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

DOI:10.15248/proc.1.877

PDF download (377.8KB)

Summary:
This paper is concerned with accurate numerical algorithms for matrix multiplication. Recently, error-free transformation for matrix multiplication is developed by the authors. It is shown that the transformation is not only useful for accurate numerical computations but also suitable for high performance computing. However, the algorithm requires much amount of working memory. In this paper, how to overcome this drawback is discussed without significant slowdown of the computational performance.

References:

[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