Rump, Siegfried M.Siegfried M.Rump2020-10-262020-10-262013-07-11Numerical Algorithms 2 (66): 309-322 (2014)http://hdl.handle.net/11420/7660Recently Miyajima presented algorithms to compute componentwise verified error bounds for the solution of full-rank least squares problems and underdetermined linear systems. In this paper we derive simpler and improved componentwise error bounds which are based on equalities for the error of a given approximate solution. Equalities are not improvable, and the expressions are formulated in a way that direct evaluation yields componentwise and rigorous estimates of good quality. The computed bounds are correct in a mathematical sense covering all sources of errors, in particular rounding errors. Numerical results show a gain in accuracy compared to previous results. © 2013 Springer Science+Business Media New York.en1572-926520132309322Springer Science Business Media B.V.Componentwise error estimatesExtra-precise residual evaluationINTLABLeast squares problemsNormal equationsUnderdetermined linear systemsMathematikJournal Article10.1007/s11075-013-9735-6Other