One of main applications of interval computations is estimating errors of indirect measurements. A quantity y is measured indirectly if we measure some quantities xi related to y and then estimate y from the results $$\tilde x_i $$ of these measurements as $$f(\tilde x_1 ,...,\tilde x_n )$$ by using a known relation f. Interval computations are used "to find the range of f(x1,...,xn) when xi are known to belong to intervals $$x_i = [\tilde x_i - \Delta _i ,\tilde x_i + \Delta _i ]$$ ," where Δi are guaranteed accuracies of direct measurements. It is known that the corresponding problem is intractable (NP-hard) even for polynomial functions f.
Reliable Computing – Springer Journals
Published: Oct 21, 2004
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