# Error Estimation for Indirect Measurements: Interval Computation Problem Is (Slightly) Harder Than a Similar Probabilistic Computational Problem

Error Estimation for Indirect Measurements: Interval Computation Problem Is (Slightly) Harder... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Error Estimation for Indirect Measurements: Interval Computation Problem Is (Slightly) Harder Than a Similar Probabilistic Computational Problem

, Volume 5 (1) – Oct 21, 2004
15 pages

/lp/springer_journal/error-estimation-for-indirect-measurements-interval-computation-clyKvZCa0I
Publisher
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1026497709529
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 21, 2004

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