# Accurate Sum and Dot Product

@article{Ogita2005AccurateSA, title={Accurate Sum and Dot Product}, author={Takeshi Ogita and Siegfried M. Rump and Shin'ichi Oishi}, journal={SIAM J. Sci. Comput.}, year={2005}, volume={26}, pages={1955-1988} }

Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or K-fold working precision, $K\ge 3$. For twice the working precision our algorithms for summation and dot product are some 40% faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition…

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