1964
DOI: 10.1007/bf01386090
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Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides

Abstract: In the spirit of ~VILKINSON'S [1, 2] backward error analysis, conditions axe established under which a given approximate solution of a system of n linear equations with n unknowns is the exact solution of a modified system whose coefficients and right-hand sides are within a given neighborhood of those of the original system.

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Cited by 329 publications
(124 citation statements)
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“…Formulas for the error computed at each step of Algorithm 1 can be obtained for instance in [18,36].…”
mentioning
confidence: 99%
“…Formulas for the error computed at each step of Algorithm 1 can be obtained for instance in [18,36].…”
mentioning
confidence: 99%
“…It is shown in [2,28] that BERR defined in Equation (1.1) measures the componentwise relative backward error of the computed solution. This means that the computed x satisfies a slightly perturbed linear system of equations (A + E)x = b + f , where |E ij | ≤ BERR · |A ij | and |f i | ≤ BERR · |b i | for all i and j.…”
Section: Error Boundsmentioning
confidence: 99%
“…Recall that the componentwise backward error of an approximate solution y to a linear system Ax = b is given by [Higham 2002, Thm. 7.3], [Oettli and Prager 1964] …”
Section: Normwise Relative Errorsmentioning
confidence: 99%