Rump, Siegfried M.Siegfried M.Rump2020-11-242020-11-242011-06-10BIT Numerical Mathematics 1 (52): 201-220 (2012-03-01)http://hdl.handle.net/11420/7915We improve the well-known Wilkinson-type estimates for the error of standard floating-point recursive summation and dot product by up to a factor 2. The bounds are valid when computed in rounding to nearest, no higher order terms are necessary, and they are best possible. For summation there is no restriction on the number of summands. The proofs are short by using a new tool for the estimation of errors in floating-point computations which cures drawbacks of the "unit in the last place (ulp)". The presented estimates are nice and simple, and closer to what one may expect. © 2011 Springer Science + Business Media B.V.en1572-912520111201220Springer Science + Business Media B.VDot productError analysisError boundsFloating-point summationRoundingUnit in the first place (ufp)Unit in the last place (ulp)InformatikMathematikJournal Article10.1007/s10543-011-0342-4Other