# 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.
.

## 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 ?
The main cause of larger values of measurement error percentage is that using 2D pictures to test morphological variation in a 3D object (skull) is an approximation that inevitably implies measurement error, i.
It is relatively inexpensive to measure the alcohol content of wine reasonably precisely, although some of the devices used may entail larger measurement errors.
More surprisingly, this policy suggestion is reinforced by the possibility of measurement error because this error will affect estimates of the output gap and the natural rate in opposite directions.
Adjustment for measurement error to account for the differences between personal and ambient exposures led to modest increases in the HRs for BS (0-3.
Two approaches were used to account for tool measurement error in crack detection sizing criteria.
Compared to the standard measurement error, the advantage of the CV is that measurement value differences resulting in particular from the large variation in individual HRs do not influence the CV.
Following two additional individual point calibrations of the sensors, the measurement error was decreased and ranged from +8 x [10.
This last estimator takes into account the measurement error present in the pseudo-panel.
In order to determine the measurement errors of the different meters, the signal reading of each meter was divided by the signal reading of the commercial reference meter A (UDT268UVA) (1) when they all measured the same 365 nm source in the figure.
This section provides an initial framework for conceptualizing the influence of assignment or task characteristics as a source of measurement error with respect to specific assessment goals and sampling strategies (Table 1).
Moreover, wideband antennas like spiral typically have 5 degrees phase tracking error in their range of view which should be added to the phase measurement error.
It points out that the small hearing losses that audiologists are trying to identify with conventional hearing tests are subject to measurement error, and that as many as 10% or more of children are identified falsely as having a noise-induced hearing loss using these methods.

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