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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The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved. www.cc.columbia.edu/cu/cup/
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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]
Allusions—Cultural, Literary, Biblical, and Historical: A Thematic Dictionary. Copyright 2008 The Gale Group, Inc. All rights reserved.

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.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
References in classic literature ?
And in this it is not likely that all are mistaken the conviction is rather to be held as testifying that the power of judging aright and of distinguishing truth from error, which is properly what is called good sense or reason, is by nature equal in all men; and that the diversity of our opinions, consequently, does not arise from some being endowed with a larger share of reason than others, but solely from this, that we conduct our thoughts along different ways, and do not fix our attention on the same objects.
I have not attempted to conceal any of my errors; they have been great, though others have erred as I have erred.
If I had drawn my will to serve them from some purer source than the memory of my errors, I should be happy indeed!
Suppose that he has been guilty of some irreparable error, from the shameful consequences of which there is no escape; a sordid nature swallows down the disgrace and survives it, the wise man drinks the hemlock and dies.
"So, in any case, suicide seemed to me to be an unpardonable error, even in the man who, through a false conception of greatness of soul, takes his life a few moments before the executioner's axe falls.
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. When we were weary with speaking, we placed in ranks those who were sufficiently instructed, and passing through them with great vessels of water, baptised them according to the form prescribed by the Church.
And that is why I can triumph over your error and your merely animal intelligence, Frederic Larsan.
To this accidental source of the error may be added the artifice of some celebrated authors, whose writings have had a great share in forming the modern standard of political opinions.
I submit to you, my fellow-citizens, these considerations, in full confidence that the good sense which has so often marked your decisions will allow them their due weight and effect; and that you will never suffer difficulties, however formidable in appearance, or however fashionable the error on which they may be founded, to drive you into the gloomy and perilous scene into which the advocates for disunion would conduct you.
(absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when it deals with separate elements of motion instead of examining continuous motion.
A few months ago I was at the old home, and I read that book again, after not looking at it for more than thirty years; and I read it with amazement at its prevailing artistic vulgarity, its prevailing aesthetic error shot here and there with gleams of light, and of the truth that Reade himself was always dimly groping for.
"Seven in 100 words in SR-generated documents contain errors; many errors involve clinical information," the authors write.