Which is the correct formula for error propagation?

Which is the correct formula for error propagation?

General Formula for Error Propagation Wemeasure x1;x2:::xn withuncertainties –x1;–x2:::–xn. The purpose of these measurements is to determine q, which is a function of x1;:::;xn: q = f(x1;:::;xn): The uncertainty in q is then –q = sµ @q @x1 –x1 ¶2 +::: + µ @q @xn –xn ¶2 10/5/01 8

Can a complex-valued back propagation algorithm be used?

This paper presents a complex-valued version of the back-propagation algorithm (called `Complex-BP’), which can be applied to multi-layered neural networks whose weights, threshold values, input and output signals are all complex numbers. Some inherent properties of this new algorithm are studied. The results may be summarized as follows.

How are significant figure rules used to propagate error?

The significant figure rules outlined in tutorial # 4 are only approximations; a more rigorous method is used in laboratories to obtain uncertainty estimates for calculated quantities. This method relies on partial derivates from calculus to propagate measurement error through a calculation.

How is the learning Convergence Theorem obtained for complex numbers?

The learning convergence theorem can be obtained by extending the theory of adaptive pattern classifiers ( Amari, 1967) to complex numbers.

When to use significant figure rules or propagation of error?

So while the significant figure rules are always to be used in any calculation, when precision matters a propagation of error analysis must also be performed to obtain an accurate prediction of the uncertainty arising from the precision of the measured quantities.

Which is the result of the propagation of uncertainty?

The result is a general equation for the propagation of uncertainty that is given as Eqn. 1.2 In Eqn. 1 f is a function in several variables, xi, each with their own uncertainty, Δ xi.

Do you propagate uncertainty through a calibration curve?

In that exercise, we did not propagate the uncertainty associated with the absorbance measurement through the calibration curve to the percent by mass. However, in most quantitative measurements, it is necessary to propagate the uncertainty in a measured value through a calibration curve to the final value being sought.

How to estimate the error of a measurement?

When attempting to estimate the error of a measurement, it is often important to determine whether the sources of error are systematic or random. A single measurement may have multiple error sources, and these may be mixed systematic and random errors. To identify a random error, the measurement must be repeated a small number of times.

Where do you find the error indicator in Excel?

If a cell contains a formula that results in an error, a triangle (an error indicator) appears in the top-left corner of the cell. You can prevent these indicators from being displayed by using the following procedure.

Which is the correct formula for percent error?

The formula is given by: The experimental value is your calculated value, and the theoretical value is your known value. A percentage very close to zero means you are very close to your targeted value, which is good.