Abstract
An estimate of the deviation of the solution of linear algebraic equations from the solution of a “frozen” system, under sufficiently small variations of the system's coefficients, is given within the framework of linear error theory.
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Literature cited
D. K. Faddeev and V. N. Faddeeva, “On natural norms for estimating the solution of a finite computational problem,” Zh. Vychisl. Mat. Mat. Fiz.,9, No. 1, 3–13 (1969).
D. K. Faddeev and V. N. Faddeeva, “On the solution of linear algebraic systems,” Zh. Vychisl. Mat. Mat. Fiz.,14, No. 3, 539–559 (1974).
E. Hansen, “On linear algebraic equations with interval coefficients,” in: Topics in Interval Analysis, E. Hansen (ed.), Clarendon Press, Oxford (1969), pp. 35–46.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 90, pp. 227–228, 1979.
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Faddeev, D.K. Estimate of a domain containing the solution of a system of linear algebraic equations. J Math Sci 20, 2068–2069 (1982). https://doi.org/10.1007/BF01680571
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DOI: https://doi.org/10.1007/BF01680571