The Effect on the Solution of a Problem of Perturbations to the data: A Study in Interval Arithmetic
D. E. Bailey · The Mathematical Gazette · 1973
It is sometimes assumed that the solution of a problem can be found to the same number of significant digits as the data. That this is not always so can be illustrated by the following example: the solution of the set of equations 123x ― 124y = 61, 248x―250y = 123 is x = 1, y = 0.5, while the solution of the perturbed set 123·01x ― 124y = 61, 248x ― 250y = 123 is x = ― 4, y = ―4·46!