Error Propagation Matrices
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propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. error propagation division When the variables are the values of experimental measurements they have error propagation calculator uncertainties due to measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the error propagation physics function. The uncertainty u can be expressed in a number of ways. It may be defined by the absolute error Δx. Uncertainties can also be defined by the
Error Propagation Chemistry
relative error (Δx)/x, which is usually written as a percentage. Most commonly, the uncertainty 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 error propagation square root 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 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]
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Error Propagation Inverse
hep-ex
Propagated Error Calculus
cited by ) NASA ADS Bookmark (what is this?) High Energy Physics - Experiment Title: Propagation of Errors https://en.wikipedia.org/wiki/Propagation_of_uncertainty for Matrix Inversion Authors: M. Lefebvre, R.K. Keeler, R. Sobie, J. White (Submitted on 17 Sep 1999) Abstract: A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 https://arxiv.org/abs/hep-ex/9909031 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with uncertain elements is sufficiently nonsingular for the calculation of the covariances of the inverted matrix elements to be reliable. Comments: 18 pages, 4 figures, figure 4 contains two eps files Subjects: High Energy Physics - Experiment (hep-ex) Journalreference: Nucl.Instrum.Meth. A451 (2000) 520-528 DOI: 10.1016/S0168-9002(00)00323-5 Citeas: arXiv:hep-ex/9909031 (or arXiv:hep-ex/9909031v1 for this version) Submission history From: Richard K. Keeler [view email] [v1] Fri, 17 Sep 1999 20:44:11 GMT (33kb) Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?) Link back to: arXiv, form interface, contact.
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