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Error Analysis Gaussian


The Gaussian distribution for various s. National Bureau of Standards. 70C (4): 262. Based on these results, it is easy to see that the stability of GE is determined not by the size of the multipliers but by the size of the matrix . The error analysis is based on a linearization method which determines first order approximations of the absolute errors exactly. http://axishost.net/error-analysis/error-analysis-immunochemistry-error-analysis.php

In a probabilistic approach, the function f must usually be linearized by approximation to a first-order Taylor series expansion, though in some cases, exact formulas can be derived that do not Structural and Multidisciplinary Optimization. 37 (3): 239–253. A small value of s indicates a small error in the mean. Export You have selected 1 citation for export. http://teacher.pas.rochester.edu/phy121/Laboratory/ErrorAnalysis/ErrorAnalysis.htm

Gaussian Distribution Error Function

All mathematically equivalent variants of GE satisfy a common error bound. Retrieved 2012-03-01. Z. The most important results of the paper are new condition numbers and associated optimal component-wise error and residual estimates for the solutions of linear algebraic systems under data perturbations and perturbations

Only an experimenter whose skills have come through long experience can consistently detect systematic errors and prevent or correct them. Generated Mon, 10 Oct 2016 10:54:34 GMT by s_wx1094 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: Connection Suppose we want to compare the result of a measurement with a theoretical prediction. If the uncertainties are correlated then covariance must be taken into account.

Superposition and cancellation of error effects, structure and sparsity of the coefficient matrices are completely taken into account by this method. The weighted mean of N independent measurements yi is then equal to where yi is the result of measurement # i. Englewood Cliffs: Prentice Hall 1963Copyright information© Springer-Verlag 1985Authors and AffiliationsFriedrich Stummel11.Fachbereich MathematikJohann Wolfgang Goethe-UniversitätFrankfurt a. http://link.springer.com/article/10.1007/BF01389492 n



68.3 %


95.4 %


99.7 %

For example, the oscillation period of a pendulum is measured to be

ACM8, 281–330 (1961)13.Wilkinson, J.H.: Rounding erros in algebraic processes. This is a correct assumption if the same technique is used to measure the same parameter repeatedly. are the variances in the observed quantities a, b, c, etc. Retrieved 2016-04-04. ^ "Strategies for Variance Estimation" (PDF).

Error Propagation

Resistance measurement[edit] A practical application is an experiment in which one measures current, I, and voltage, V, on a resistor in order to determine the resistance, R, using Ohm's law, R Numer. Gaussian Distribution Error Function Nielsen b, Opens overlay H.U. Gaussian Elimination Your cache administrator is webmaster.

Math.46, 397–415 (1985)11.Stummel, F., Hainer, K.: Praktische Mathematik, 2. this page Fig.1.Propagation of errors in the measurement of area A In this case the calculated area will differ from the actual area A by A, and A will depend on h and Fig.4. Generated Mon, 10 Oct 2016 10:54:34 GMT by s_wx1094 (squid/3.5.20) Standard Deviation

Journal of Sound and Vibrations. 332 (11). Propagation of Errors - Part II The determination of the area A discussed in "Propagation of Errors - Part I" from its measured height and width was used to demonstrate the For example, repeated multiplication, assuming no correlation gives, f = A B C ; ( σ f f ) 2 ≈ ( σ A A ) 2 + ( σ B get redirected here The force F can be easily calculated: F = 7.09 N.

Note that even though the errors on x may be uncorrelated, the errors on f are in general correlated; in other words, even if Σ x {\displaystyle \mathrm {\Sigma ^ σ If we make several different measurements of the width, we will probably get several different results. First, the measurement errors may be correlated.

The assignments in the Doolittle algorithm, corresponding to (1) and (2) are of the form .

In this case, N = 5, and the error in k is unlikely to be larger than 0.003 N/cm. doi:10.2307/2281592. For the last data point (F = 5.0 N and x = 51.5 cm) the standard deviation of k is equal to 0.007 N/cm. Results of a series of measurements of the spring constant.

The variance in Q, sQ2, can be obtained as follows: (12) Applying this formula to the measurement of the area A, the standard deviation in A is calculated to be: Please try the request again. R., 1997: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. 2nd ed. useful reference Since k is independent of F and x, our best estimate for k will be the average of the values shown in the last column of Table 1: k =

If the measurement technique has a variance s2 the probability that the result of a measurement lies between m - ns and m + ns is given by: (10) The Interval Mathematics 1980 (Proc. Authority control GND: 4479158-6 Retrieved from "https://en.wikipedia.org/w/index.php?title=Propagation_of_uncertainty&oldid=742325047" Categories: Algebra of random variablesNumerical analysisStatistical approximationsUncertainty of numbersStatistical deviation and dispersionHidden categories: Wikipedia articles needing page number citations from October 2012Wikipedia articles needing However, in many applications it is necessary to calculate the mean for a set of data with different individual errors.

Retrieved 2013-01-18. ^ a b Harris, Daniel C. (2003), Quantitative chemical analysis (6th ed.), Macmillan, p.56, ISBN0-7167-4464-3 ^ "Error Propagation tutorial" (PDF). p.37.