Error Propagation Define
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Error Propagation Example
Computing © A Dictionary of Computing 2004, originally published by Oxford University Press 2004. error propagation error propagation division A term that refers to the way in which, at a given stage of a calculation, part of the error arises out of the error at a previous
Error Propagation Physics
stage. This is independent of the further roundoff errors inevitably introduced between the two stages. Unfavorable error propagation can seriously affect the results of a calculation. The investigation of error propagation in simple arithmetical operations is used as the basis for the detailed analysis of more extensive calculations. The way in which uncertainties in the data error propagation calculus propagate into the final results of a calculation can be assessed in practice by repeating the calculation with slightly perturbed data. Cite this article Pick a style below, and copy the text for your bibliography. MLA Chicago APA "error propagation." A Dictionary of Computing. . Encyclopedia.com. 11 Oct. 2016
propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the
Error Propagation Khan Academy
function. The uncertainty u can be expressed in a number of ways. It may be defined by
Error Propagation Average
the absolute error Δx. Uncertainties can also be defined by the relative error (Δx)/x, which is usually written as a percentage. Most commonly, the uncertainty error propagation chemistry on a quantity is quantified in terms of the standard deviation, σ, the positive square root of variance, σ2. The value of a quantity and its error are then expressed as an interval x ± u. If the statistical probability distribution http://www.encyclopedia.com/doc/1O11-errorpropagation.html of the variable is known or can be assumed, it is possible to derive confidence limits to describe the region within which the true value of the variable may be found. For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are ± one standard deviation from the value, that is, there is approximately a 68% probability that the true value lies in the region x ± σ. If the uncertainties are correlated then covariance must be taken https://en.wikipedia.org/wiki/Propagation_of_uncertainty into account. Correlation can arise from two different sources. First, the measurement errors may be correlated. Second, when the underlying values are correlated across a population, the uncertainties in the group averages will be correlated.[1] Contents 1 Linear combinations 2 Non-linear combinations 2.1 Simplification 2.2 Example 2.3 Caveats and warnings 2.3.1 Reciprocal 2.3.2 Shifted reciprocal 3 Example formulas 4 Example calculations 4.1 Inverse tangent function 4.2 Resistance measurement 5 See also 6 References 7 Further reading 8 External links Linear combinations[edit] Let { f k ( x 1 , x 2 , … , x n ) } {\displaystyle \ ρ 5(x_ ρ 4,x_ ρ 3,\dots ,x_ ρ 2)\}} be a set of m functions which are linear combinations of n {\displaystyle n} variables x 1 , x 2 , … , x n {\displaystyle x_ σ 7,x_ σ 6,\dots ,x_ σ 5} with combination coefficients A k 1 , A k 2 , … , A k n , ( k = 1 … m ) {\displaystyle A_ σ 1,A_ σ 0,\dots ,A_ ρ 9,(k=1\dots m)} . f k = ∑ i n A k i x i or f = A x {\displaystyle f_ ρ 5=\sum _ ρ 4^ ρ 3A_ ρ 2x_ ρ 1{\text{ or }}\mathrm ρ 0 =\mathrm σ 9 \,} and let the variance-covariance matrix on x be denoted by Σ x {\displaystyle \mathrm {\Sigma ^ σ 1} \,} . Σ x = ( σ 1 2 σ 12 σ 13 ⋯
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