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 It might be outdated or ideologically biased.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 periodicals archive ?
The very small differences among parameters of the individual samples could be attributed to experimental errors. The difference between WAXS and DSC crystallinities could be attributed to the intrinsic differences between the two methods.
The degree of freedom for experimental error is [f.sub.e] calculated by the total degree of freedom minus degrees of freedom for all factors, that is, [f.sub.e] = [f.sub.T] - [f.sub.A] - [f.sub.B] - [f.sub.C]- [f.sub.D] - [f.sub.E] - [f.sub.G] = 17-2-2-2-2-2-2-2 = 5.
Sum of squares, mean squares and percentages of total variation of G, E, G x E interaction and experimental error (replications) for various traits in upland cotton.
Mean square of Source of Variation Degree of phenologycal traits freedom Days up to the Days up to spike emergence flowering (A) Replication 2 129.744 122.133 (B) Stress levels 2 15.744 16.233 Cultivar 9 44.548 * 44.919 ** A B 18 6.930 6.307 Experimental Error 58 10..78 10.467 CV% _ 2.60 2.45 Mean square of Source of Variation phenologycal traits Days up to Filling of the physiologycal maturity grain period (A) Replication 131.700 34.144 (B) Stress levels 246.400 * 347.144 ** Cultivar 30.222 ** 17.111 * A B 8.437 12.678 Experimental Error 12.171 7.340 CV% 2.09 7.72 * And **: significant at the Probability levels of 5 and 1 Percent respectively Table 3: Mean of the phenologycal traits of treatments.
In addition, three central replicates were also added to the experimental design to calculate pure experimental error. As the analysis of variance reveals that quadratic terms were effective on bleaching capacity of Arguvan bentonite, the orthogonal central composite design was planned to estimate quadratic terms separately.
Thus, many measurements are given together with experimental error. For this reason, even if we know that a given theory is not perfect, it still can be regarded as a correct theory for cases where the theory's errors are smaller than the experimental errors.
By converting user-dependent digestion protocols to a streamlined, automated platform, experimental error is minimized run-to-run and the coefficients of variation fall well below 10%.
For each value of moisture content, the weighing was made three times with different powders to calculate the experimental error.

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