iterationn.

/ɪtəˈreɪʃən/

Forms: Also 1500s yt-, itt-.

Etymology: < Latin iterātiōn-em, noun of action from iterāre to iterate v. Compare French itération (1488 in Godefroy).

The action of iterating or repeating, or process of being iterated.

a. Repetition of an action or process (now usually implying frequency or long continuance); repeated performance; an instance of this. Formerly said esp. of readministering a sacrament.

ΘΚΠ

the world > action or operation > repeating > [noun]

reiteration?a1425

iteration1477

itering1530

repetition?1550

iteratinga1593

repeat1667

repeating1671

ringing of changes1734

dittoism1884

ofteninga1889

1477 T. Norton Ordinall of Alchimy vi, in E. Ashmole Theatrum Chem. Britannicum (1652) 100 The multitude of their Iteration.

?1550 J. Bale Apol. agaynste Papyst 18 Than grewe it into a name and use amonge that sort (as amonge the sectes of owr tyme the iteracyon of baptysme).

1694 W. Salmon Pharmacopœia Bateana i. xix. 551/2 For the three or four Iterations, the Regulus becomes apparently more bright and pure.

1790 W. Paley Horæ Paulinæ (1825) 159 The rules of good writing taught the ear to be offended with the iteration of the same sound.

1845 S. Austin tr. L. von Ranke Hist. Reformation in Germany (ed. 2) I. 3 The lifeless iteration of misunderstood doctrines and rites, which kill the soul.

1872 W. Minto Man. Eng. Prose Lit. Introd. 30 A person of strong tender feeling is not easily offended by the iteration of pathetic images.

b. Mathematics. The repetition of an operation upon its product, as in finding the cube of a cube; esp. the repeated application of a formula devised to provide a closer approximation to the solution of a given equation when an approximate solution is substituted in the formula, so that a series of successively closer approximations may be obtained; a single application of such a formula; also, the formula itself.

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > process of calculating > use of repeated procedure

recursion1895

iteration1924

1901 in N.E.D.

1924 E. T. Whittaker & G. Robinson Calculus of Observ. vi. 79 In 1674 a method depending on a new principle, the principle of iteration, was communicated in a letter from Gregory to Collins.

1941 London, Edinb. & Dublin Philos. Mag. 7th Ser. 32 374 After a few iterations the values of e_r much less than unity will hardly affect the results.

1960 G. N. Lance Numerical Methods for High Speed Computers i. 8 Whichever criterion is used to determine the end of the iteration, it is clear that the orders to evaluate f(x_r) and f(x_{r + 1}) are identical except that x_{r + 1} is used instead of x_r. This kind of modification is made extremely simple on high-speed computers.

1968 E. T. Copson Metric Spaces viii. 115 The Newton-Raphson iteration x_{n + 1} = x_n − f(x_n)/f′(x_n) for solving the equation f(x) = 0.

c. Roman Law. (See quot. 1880.)

ΚΠ

1880 J. Muirhead tr. Ulpian Rules iii, in tr. Gaius Institutes 369 By iteration he becomes a Roman citizen who, having been made a latin after he had passed the age of thirty, is anew formally manumitted by the person who had the quiritarian right in him when a slave.

2. The repetition of something said; repeated utterance or assertion.

ΘΚΠ

the mind > language > speech > repetition > [noun]

replication?c1400

repetition?a1425

repeatingc1443

renovelling1483

regressiona1500

iteration1530

repeat1556

ingemination1576

iteratinga1593

iterancea1616

redoublinga1665

restatement1790

troll1790

repeatal1822

catching up1847

rewording1849

re-enunciation1855

iterancy1889

the mind > language > statement > [noun] > renewed or repeated

iteration1530

1530 J. Palsgrave Lesclarcissement 333 After yteracyons of the pronowne they use ever moij.

1556 J. Heywood Spider & Flie Concl. 50 Tedius Iteration therof I let passe.

1634 T. Heywood & R. Brome Late Lancashire Witches iiii. sig. H2 I will not aggravate thy griefe too much, By Needles iteration.

1759 S. Johnson Idler 6 Oct. 313 Any curious iteration of the same word.

1886 Manch. Examiner 29 Jan. 5/2 The House was told with suspicious iteration that the Government had nailed their colours to the mast.

This entry has not yet been fully updated (first published 1900; most recently modified version published online December 2020).

单词	iteration
释义	iterationn. /ɪtəˈreɪʃən/ Forms: Also 1500s yt-, itt-. Etymology: < Latin iterātiōn-em, noun of action from iterāre to iterate v. Compare French itération (1488 in Godefroy). The action of iterating or repeating, or process of being iterated. 1. a. Repetition of an action or process (now usually implying frequency or long continuance); repeated performance; an instance of this. Formerly said esp. of readministering a sacrament. ΘΚΠ the world > action or operation > repeating > [noun] reiteration?a1425 iteration1477 itering1530 repetition?1550 iteratinga1593 repeat1667 repeating1671 ringing of changes1734 dittoism1884 ofteninga1889 1477 T. Norton Ordinall of Alchimy vi, in E. Ashmole Theatrum Chem. Britannicum (1652) 100 The multitude of their Iteration. ?1550 J. Bale Apol. agaynste Papyst 18 Than grewe it into a name and use amonge that sort (as amonge the sectes of owr tyme the iteracyon of baptysme). 1694 W. Salmon Pharmacopœia Bateana i. xix. 551/2 For the three or four Iterations, the Regulus becomes apparently more bright and pure. 1790 W. Paley Horæ Paulinæ (1825) 159 The rules of good writing taught the ear to be offended with the iteration of the same sound. 1845 S. Austin tr. L. von Ranke Hist. Reformation in Germany (ed. 2) I. 3 The lifeless iteration of misunderstood doctrines and rites, which kill the soul. 1872 W. Minto Man. Eng. Prose Lit. Introd. 30 A person of strong tender feeling is not easily offended by the iteration of pathetic images. b. Mathematics. The repetition of an operation upon its product, as in finding the cube of a cube; esp. the repeated application of a formula devised to provide a closer approximation to the solution of a given equation when an approximate solution is substituted in the formula, so that a series of successively closer approximations may be obtained; a single application of such a formula; also, the formula itself. ΘΚΠ the world > relative properties > number > mathematics > [noun] > mathematical enquiry > process of calculating > use of repeated procedure recursion1895 iteration1924 1901 in N.E.D. 1924 E. T. Whittaker & G. Robinson Calculus of Observ. vi. 79 In 1674 a method depending on a new principle, the principle of iteration, was communicated in a letter from Gregory to Collins. 1941 London, Edinb. & Dublin Philos. Mag. 7th Ser. 32 374 After a few iterations the values of e_r much less than unity will hardly affect the results. 1960 G. N. Lance Numerical Methods for High Speed Computers i. 8 Whichever criterion is used to determine the end of the iteration, it is clear that the orders to evaluate f(x_r) and f(x_{r + 1}) are identical except that x_{r + 1} is used instead of x_r. This kind of modification is made extremely simple on high-speed computers. 1968 E. T. Copson Metric Spaces viii. 115 The Newton-Raphson iteration x_{n + 1} = x_n − f(x_n)/f′(x_n) for solving the equation f(x) = 0. c. Roman Law. (See quot. 1880.) ΚΠ 1880 J. Muirhead tr. Ulpian Rules iii, in tr. Gaius Institutes 369 By iteration he becomes a Roman citizen who, having been made a latin after he had passed the age of thirty, is anew formally manumitted by the person who had the quiritarian right in him when a slave. 2. The repetition of something said; repeated utterance or assertion. ΘΚΠ the mind > language > speech > repetition > [noun] replication?c1400 repetition?a1425 repeatingc1443 renovelling1483 regressiona1500 iteration1530 repeat1556 ingemination1576 iteratinga1593 iterancea1616 redoublinga1665 restatement1790 troll1790 repeatal1822 catching up1847 rewording1849 re-enunciation1855 iterancy1889 the mind > language > statement > [noun] > renewed or repeated iteration1530 1530 J. Palsgrave Lesclarcissement 333 After yteracyons of the pronowne they use ever moij. 1556 J. Heywood Spider & Flie Concl. 50 Tedius Iteration therof I let passe. 1634 T. Heywood & R. Brome Late Lancashire Witches iiii. sig. H2 I will not aggravate thy griefe too much, By Needles iteration. 1759 S. Johnson Idler 6 Oct. 313 Any curious iteration of the same word. 1886 Manch. Examiner 29 Jan. 5/2 The House was told with suspicious iteration that the Government had nailed their colours to the mast. This entry has not yet been fully updated (first published 1900; most recently modified version published online December 2020). < n.1477
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