error

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error,

in law: see appealappeal,
in law, hearing by a superior court to consider correcting or reversing the judgment of an inferior court, because of errors allegedly committed by the inferior court.
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Error

 

in automatic control systems, the difference between the set point and the actual value of the quantity being controlled in a control process. At any given moment, the error can be regarded as the sum of the static error—the error under steady-state conditions—and the dynamic error—the error in a transient response. In the statistical analysis of automatic control systems, the distinction between steady-state and transient errors loses its meaning, and the quality of performance of such a system is evaluated by criteria associated with the probability characteristics of the error. An example of such a criterion is the minimum mean-square error.


Error

 

When a number a is taken as the approximate value of a quantity whose exact value is x, the error of a is the difference xa, which is also called the absolute error. The ratio of xa to a is called the relative error. An error is usually characterized by indicating its maximum possible value. The maximum possible value of the absolute error is the number Δ (a) such that ǀxaǀ ≤ Δ(a). The maximum possible value of the relative error is the number δ(a) such that

The maximum values of relative errors are often expressed as percentages. The numbers Δ(a) and δ(a) are taken as small as possible.

If a is the approximate value of x with a maximum absolute error of Δ(a), this fact can be written x = a ± Δ(a). The analogous expression for the relative error is x = a(1 ± δ(a)).

The maximum values of the absolute and relative errors indicate the maximum possible divergence between x and a. In addition to these values, an error is often characterized by the nature of its origin and by the frequency of occurrence of different values of xa. The methods of probability theory are used in this approach to errors.

The error of the result in the numerical solution of a problem is caused by inaccuracies intrinsic to the formulation of the problem and to the means used to solve it. Errors stemming from the inaccuracy of a mathematical description of an actual process—for example, from an inaccurate statement of the original data—are said to be inherent errors. Errors of method arise because of the inaccuracy of the method used in solving the problem. Computational errors are the result of inaccuracies in computations.

When computations are performed, initial errors pass in succession from operation to operation, accumulating and giving rise to new errors. The appearance and propagation of errors in computational work are studied by numerical analysis.

REFERENCES

Berezin, I. S., and N. P. Zhidkov. Metody vychislenii, 3rd ed., vol. 1. Moscow, 1966.
Bakhvalov, N. S. Chislennye metody. Moscow, 1973.

G. D. KIM

error

[′er·ər]
(computer science)
An incorrect result arising from approximations used in numerical methods, rather than from a human mistake or computer malfunction.
(science and technology)
Any discrepancy between a computed, observed, or measured quantity and the true, specified, or theoretically correct value of that quantity.

Error

Breeches Bible, the
the Geneva Bible, so dubbed because it stated that Adam and Eve made themselves breeches. [Br. Hist.: Brewer Dictionary, 101]
Cortez
alluded to in a poem by Keats, mistaken for Balboa, as discoverer of Pacific Ocean. [Br. Poetry: “On First Looking into Chapman’s Homer”]
Wicked Bible, the
misprinted a commandment as “Thou shalt commit adultery.” [Br. Hist.: Brewer Dictionary, 102]
seacoast of Bohemia
Shakespearean setting in a land with no seacoast. [Br. Drama: Shakespeare The Winter’s Tale, III,iii]

error

(1)
A discrepancy between a computed, observed, or measured value or condition and the true, specified, or theoretically correct value or condition.

error

(programming)
A mental mistake made by a programmer that may result in a program fault.

error

(3)
(verb) What a program does when it stops as result of a programming error.
References in periodicals archive ?
Section 2 presents data models with test costs and misclassification costs as well as measurement errors. Section 3 describes the computational model, namely, covering-based rough set model with measurement errors.
We assume that year, cohort and age variables do not suffer from measurement error, while years-of-schooling does.
CTT, which assumes that an observed score may be decomposed into an expected true score and random error (Crocker & Algina, 1986), not only fails to consider multiple sources of error simultaneously but also fails to investigate interaction effects across sources of measurement error. Generalizability theory, or G-theory (Cronbach, Glesser, Nanda, & Rajaratman, 1972), has less restrictive assumptions than CTT and in many respects supplants this framework since it has been repeatedly demonstrated that investigations of reliability under CTT are special cases of G-theory designs (e.g., Brennan, 2011).
Figure 8 shows the RMS error of azimuth and elevation in the frequency band of 2 to 12 GHz with step 50 MHz in the presence of 35 degrees of phase measurement error. It should be mentioned that neural networks are trained every 100 MHz in the frequency interval.
(11) Trend growth is also subject to measurement error, which is ignored in this analysis.
Temperature measurements show that temperature measurement errors of sensors A, B, D2 and C were within acceptable ranges and mostly within the accuracies claimed by the manufacturers.
By comparison of the paste-filling capacity measured by the flow sensor with the paste-filling capacity of the mined area, the measurement error of the sensor [DELTA][delta](t) is obtained.
The larger this ratio, the less the effect of measurement errors. For example, if error-free [BV.sup.i] = 51 and [V.sub.inf] = 11, then the error-free [[Hb].sub.b] ratio in (2) would be 1.2 (20% dilution).
This method has a reported accuracy of +/- 0.2% ABV Random measurement error at this rate cannot account for the patterns recorded in our data.
Once the cause for the systematic measurement error is found and corrected, the test is recalibrated.
When we combine these two contrasting effects of measurement error, the model suggests that the optimal response to the measured natural rate is c = 1.21.

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