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This paper pays attention to the question, in which cases the verification of the solution of the linear system by the backward substitution can be regarded as the sufficient criterion to take the founded solution for aproximation of the exact solution. It is investigated, how great is the influence of ill conditioning of the matrix of the set on the failing of this criterion.
[1] Tupper: Ill conditioned linear equations. Math. Gaz., vol. XLII, 1958, str. 299 - 300. DOI 10.2307/3610462
[2] Демидович-Марон: Основы вычислительной математики. Москва 1963, Физматтиз. Zbl 1145.93303
[3] Фаддеев-Фаддеева: Вычислительные методы линейной алгебры. Москва 1963, Физматгиз. Zbl 1145.93303
[4] Neumann-Goldstine: Numerical inverting of matrices of high order. BAMS., 1947/2, November.
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