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 classic literature ?
There still remains to me the proud humility of repentance; I will find some sphere of life where I can expiate the errors to which you, the mediator between Heaven and me, have shown no mercy.
If I had drawn my will to serve them from some purer source than the memory of my errors, I should be happy indeed
The next thing to observe (although I do not personally doubt that most of our judgments of perception are true) is that it is very difficult to define any class of such judgments which can be known, by its intrinsic quality, to be always exempt from error.
There is no way hitherto discovered of wholly eliminating the risk of error, and no infallible criterion.
We erected our tent, and placed our altar under some great trees, for the benefit of the shade; and every day before sun-rising my companion and I began to catechise and instruct these new Catholics, and used our utmost endeavours to make them abjure their errors.
Points, Lines, Squares, Cubes, Extra-Cubes -- we are all liable to the same errors, all alike the Slaves of our respective Dimensional prejudices, as one of your Spaceland poets has said,'One touch of Nature makes all worlds akin'.
They are related because a larger body diagonal error indicates a larger volumetric error, but the ratio is not exactly a one-to-one correspondent.
The P-element provides Proportional error correction.
In an exemplary way, Louise Labe turns the lover/poet's error into a renewed relation with canonical texts.
Other error-prone sites included the Office of National Statistics, the Department of Health, and the Department of Trade & Industry, which has more than 2,700 broken links on the site alone--an "unacceptable error level,' according to the report.
Omission error-failure to administer an ordered dose-was the most common type of error (29% of all errors), followed by improper dose (2 1%) and prescribing errors (14%).