Ogita, TakeshiTakeshiOgitaRump, Siegfried M.Siegfried M.RumpOishi, Shin’ichiShin’ichiOishi2021-02-022021-02-022005-11-25SIAM Journal on Scientific Computing 6 (26): 1955-1988 (2005-11-25)http://hdl.handle.net/11420/8670Algorithms 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 AT-fold working precision, K ≥ 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, subtraction, and multiplication of floating-point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.en1095-71972005619551988Accurate dot productAccurate summationFast algorithmsHigh precisionVerified error boundsInformatikMathematikJournal Article10.1137/030601818Other