Rump, Siegfried M.Siegfried M.Rump2020-11-132020-11-132015-07-01Nonlinear Theory and Its Applications, IEICE 3 (6): 360-363 (2015)http://hdl.handle.net/11420/7826Standard error estimates in numerical linear algebra are often of the form γk|R||S| where R,S are known matrices and γk:=ku/(1-u) with u denoting the relative rounding error unit. Recently we showed that for a number of standard problems γk can be replaced by ku for any order of computation and without restriction on the dimension. Such problems include LU- and Cholesky decomposition, triangular system solving by substitution, matrix multiplication and more. The theoretical bound implies a practically computable bound by estimating the error in the floating-point computation of ku|R||S|. Standard techniques, however, imply again a restriction on the dimension. In this note we derive simple computable bounds being valid without restriction on the dimension. As the bounds are mathematically rigorous, they may serve in computer assisted proofs.en2185-410620153360363InformatikMathematikJournal Article10.1587/nolta.6.360Other