The algebraic properties of external numbers formalize common error analysis, with rules for calculation which are a sort of mellowed form of the axioms for real numbers. We model the propagation of errors in matrix calculus by the calculus of matrices with external numbers, and study its ...
performing the operation on the initial measurements, knowing the value(s) of the uncertainty of the measurements, calculating error of propagation based on the operation being used, and showing the initial measurements' calculation +/- the error of propagation. The final result should be represented...
The error propagation formulae depend on the mathematical operation used for calculation. Considering the mathematical operation addition: Let’s say you measured the length of two rods (X ±ΔX) as 2.00 ± 0.03 m and (Y ±ΔY) is 0.88 ± 0.04 m. This means that the sum of lengths of...
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2×2 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 ca...
This calculation will only work when the partial derivatives are 1. The formula changes slightly when x is a product (x = uv) or quotient (x = u/v): Example question #2: A shipping container is 12 x 10 x 8 feet with an uncertainty of 0.1ft. What is the uncertainty in the volume...
Sigma used as a statistical calculation assumes a mean value and the deviations from the mean. This paper describes the propagation of error throughout calculations to the end result. As an example, take the numbers 1, 2, and 3. This could be a population of data points. You would...
The result of a first calculation may be determined by one of two alternative calculations. Each of the alternative calculations has an error associated therewith (due to factors such as measurement imprecision, rounding, etc.), and these errors propagate to the first calculation. However, there ...
In many electromagnetic problems such as: calculation of scattering parameters, determination of magnetic field gradients, or in the modeling of electromagnetic interference, the Fourier transform is a part of the algorithm used. The paper proposes an analytical procedure to calculate the random error ...
Calculation of uncertainty propagation using adjoint equations. International Journal of Computational Fluid Dynamics 2003; 17(4):283-288.A. K. ALEKSEEV and I. M. NAVON, "Calculation of Uncertainty Propagation using Adjoint Equations," Int. J. Comput. Fluid Dyn., 17(4), 283-288 (2003)....
For the more, the error transmission process in calculation is analyzed. 针对施工场地狭小 ,无法建立稳定测站的情况 ,提出在移动点上通过观测角度变化 ,间接计算出该点水平位移的方法 ,进一步分析了计算过程中的误差传递 ,确定了观测精度 ,提出了选择相应仪器的标 3. With the water\|rock chemical equilibrium...