Oishi, Shin’ichiShin’ichiOishiOgita, TakeshiTakeshiOgitaRump, Siegfried M.Siegfried M.Rump2021-01-252021-01-252009-10Japan Journal of Industrial and Applied Mathematics 2/3 (26): 465-476 (2009)http://hdl.handle.net/11420/8567This paper treats a linear equation Aυ = b, where A ∈ F n×n and b ∈ Fn. Here, F is a set of floating point numbers. Let u be the unit round-off of the working precision and κ(A) = ∥A∥∞∥A-1∥∞ be the condition number of the problem. In this paper, ill-conditioned problems with 1 < uκ(A) < ∞ are considered and an iterative refinement algorithm for the problems is proposed. In this paper, the forward and backward stability will be shown for this iterative refinement algorithm.en1868-937X20092/3465476Springer NatureIll-conditioned linear systemsIterative refinementVerified numerical computationInformatikMathematikJournal Article10.1007/BF03186544Other