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Error and uncertainty
Published in W. Schofield, M. Breach, Engineering Surveying, 2007
True error (εx) similarly can never be found, for it consists of the true value (X) minus the observed value (x), i.e. X − x = εx Relative error is a measure of the error in relation to the size of the measurement. For instance, a distance of 10 m may be measured with an error of ±1 mm, whilst a distance of 100 m may also be measured to an accuracy of ±1 mm. Although the error is the same in both cases, the second measurement may clearly be regarded as more accurate. To allow for this, the term relative error (Rx) may be used, where Rx = εx/x Thus, in the first case x = 10 m, εx= ±1 mm, and therefore Rx = 1/10 000; in the second case, Rx = 1/100 000, clearly illustrating the distinction. Multiplying the relative error by 100 gives the percentage error. ‘Relative error’is an extremely useful definition, and is commonly used in expressing the accuracy of linear measurement. For example, the relative closing error of a traverse is usually expressed in this way. The definition is clearly not applicable to expressing the accuracy to which an angle is measured, however.
Computation
Published in H. G. Davies, G. A. Hicks, Mathematics for scientific and technical students, 2014
The modulus is used in (i) because the error may be positive or negative. The relative error is a useful indicator of error because it is important to compare the size of the error to the correct value. For example, an error of I mm in a measurement of 20 mm represents a relative error of 1/20 x 100 = 5% which is large. On the other hand the same error of 1 mm in a measurement of 1 m represents a relative error of 0.05%, which is small.
Error Analysis
Published in James P. Howard, Computational Methods for Numerical Analysis with R, 2017
Unlike the absolute error, the relative error is unitless. It is the ratio of the error to the true value and the units cancel each other. This has advantages. The unitless error estimate can be compared across different systems, if otherwise appropriate. Or the relative error can be interpreted as a percentage of the true value. Reducing relative error has a larger impact on correctness than reducing the absolute error, when considered as a percentage of the true value.
Analysis of sediment transport in sewer pipes using a coupled CFD-DEM model and experimental work
Published in Urban Water Journal, 2019
Maryam Alihosseini, Paul Uwe Thamsen
The critical velocity to initiate the motion of coarse gravel was also obtained numerically. Table 3 summarizes the experimental and numerical values of the critical velocity for different bed roughnesses. The relative error between experimental and numerical results is within an agreeable range (≤ 15%). Figure 6 graphically displays the flow velocity at the threshold moment of transport of coarse gravel for the three bed roughness sizes in CFD-DEM and experiment. It can be observed that the required velocity for initiating the motion of sediments increased with increasing bed roughness. Both numerical and experimental results indicate a linear correlation in this respect. Although, in the experiment, the correlation coefficient (R2 = 0.92) is larger than in the CFD-DEM (R2 = 0.86).
Exponential Time Differencing Schemes for Fuel Depletion and Transport in Molten Salt Reactors: Theory and Implementation
Published in Nuclear Science and Engineering, 2022
Zack Taylor, Benjamin S. Collins, G. Ivan Maldonado
where is the number of elements in the solution domain. Sometimes it is more meaningful to show an absolute error instead of a relative error. The results explicitly state whether a relative or absolute difference is used. Run time is also reported for some tests and is reported as the wall time for calling the solve function. This includes the time to build the matrix, run the solution algorithm, and unpack the solution. For problems with multiple time steps, the matrix was rebuilt before each time step to update the deferred correction source term. While these run times are reported with no standard deviation, some changes are to be expected when running problems multiple times or on different machines.
Truncation Based Approximate Multiplier For Error Resilient Applications
Published in International Journal of Electronics Letters, 2022
Prashil Parekh, Samidh Mehta, Pravin Mane
In this paper, comparisons of three error parameters - relative error, mean relative error distance and acceptance probability for 100,000 random numbers are presented for both the schemes of approximate multipliers in the following sections. Relative error is defined as percentage ratio of the difference between exact value and approximate value to the exact value. Mean relative error distance is the average of all the relative errors. Acceptance probability is the probability that the multiplication output produced by the approximate multiplier is within 1% of the relative error.