Accurate Sum and Dot Product

By Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi. SIAM Journal on Scientific Computing, 2005

456 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Hardware and Architecture, Signal Processing

View Paper: https://www.semanticscholar.org/paper/85216d293b272caf6d8677990d0d636cd56934a4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. R. Townsend
2. Siegfried M. Rump

In Hardware and Architecture

1. Siegfried M. Rump

In Signal Processing

1. Siegfried M. Rump

Citations in the corpus

• MODULES FOR EXPERIMENTS IN STELLAR ASTROPHYSICS (MESA): BINARIES, PULSATIONS, AND EXPLOSIONS (2015, methodology): “Methods for accurate summation within the bounds of a given arithmetic remain an active field of research (e.g., Demmel & Hida 2003; McNamee 2004; Ogita et al. 2005; Rump et al. 2008; Graillat & Ménissier-Morain 2012; Collange et al. 2014).”
• Inversion of extremely Ill-conditioned matrices in floating-point (2009, methodology): “This operation is executed by firstly transforming the dot products into sums, which is error-free, and secondly by applying Algorithm 2.3 (SumKK) to the sums.”