WordNet

(computer science) a single execution of a set of instructions that are to be repeated; "the solution took hundreds of iterations" (同)loop
(computer science) executing the same set of instructions a given number of times or until a specified result is obtained; "the solution is obtained by iteration" (同)looping
doing or saying again; a repeated performance
the act of doing or performing again (同)repeating
the repeated use of the same word or word pattern as a rhetorical device
do over; "They would like to take it over again" (同)take_over
an event that repeats; "the events today were a repeat of yesterdays" (同)repetition
to say again or imitate; "followers echoing the cries of their leaders" (同)echo
to say, state, or perform again; "She kept reiterating her request" (同)reiterate, ingeminate, iterate, restate, retell
reproduce or make an exact copy of; "replicate the cell"; "copy the genetic information" (同)copy
several time; "it must be washed repeatedly"
characterized by repetition; "repetitive movement" (同)repetitious
in a repetitive manner; "this type of border display is used repetitively in advertising"
use of the same consonant at the beginning of each stressed syllable in a line of verse; "around the rock the ragged rascal ran" (同)initial rhyme, beginning rhyme, head rhyme
a transcription from one alphabet to another

PrepTutorEJDIC

反復,繰り返し
(…‘を')『繰り返すこと,反複すること』;(…の)暗唱《+『of』+『名』》 / (;の)写し,複写,模写(copy),模倣《+『of』+『名』》
〈自分がすでに一度言ったこと)‘を'『繰り返して言う』 / 〈他人の言ったこと〉‘を'おうむ返しに言う;…‘を'他の人に繰り返して言う / …‘を'『暗記して言う』,暗唱する / …‘を'繰り返して行う(do again) / (食べたあとで)〈食物の〉味が残る / 〈小数が〉循環する / 繰り返すこと,反復すること / 繰り返されるもの,(公演の)再演;(番組の)再放送 / 反復楽節;反復記号(∥: :∥)
(統計)実施・(楽)1［数］オクターブ高い［低い］音・（葉などが）折返った・反復した・再生する・模写［複製］する; 折返す.〈葉など〉‘を'折り返す,曲げ返す・…‘を'繰り返す・細胞分裂で再生する
繰り返して,再三再四
=repetitious
頭韻,頭声[法](韻律で,Care killed the cat.のように同じ音,まれに同じ文字で始まる語を2回以上繰り返すこと)
繰り返し,反復(repetition)
字訳,音訳

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/07/21 18:48:16」(JST)

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[Wiki en表示]

A pentagon iteration. Connecting alternate corners of a regular pentagon produces a pentagram which encloses a smaller inverted pentagon. Iterating the process produces a sequence of nested pentagons and pentagrams and also demonstrates recursion (in the sense of nested self-similarity).^[1]

Iteration is the act of repeating a process with the aim of approaching a desired goal, target or result. Each repetition of the process is also called an "iteration", and the results of one iteration are used as the starting point for the next iteration. The pentagon on the right also is a good example of how iteration relates to recursion. Although iteration is used, for example, to parse a linked list, recursion is required when we step up to binary trees. The pentagon demonstrates both.^[2]

Mathematics

Iteration in mathematics may refer to the process of iterating a function i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviours and difficult problems - for examples, see the Collatz conjecture and juggler sequences.

Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a common use and a well-known example.

Computing

Iteration in computing is the repetition of a block of statements within a computer program. It can be used both as a general term, synonymous with repetition, and to describe a specific form of repetition with a mutable state. Confusingly, it may also refer to any repetition stated using an explicit repetition structure, regardless of mutability.

When used in the first sense, recursion is an example of iteration, but typically using a recursive notation, which is typically not the case for iteration.

However, when used in the second (more restricted) sense, iteration describes the style of programming used in imperative programming languages. This contrasts with recursion, which has a more declarative approach.

Used in the third sense, repetitions using while or for loops as well as those using map or fold functions may be considered iterations.

Here is an example of iteration relying on destructive assignment, in imperative pseudocode:

a = 0
for i from 1 to 3        // loop three times
{
  a = a + i              // add the current value of i to a
}
print a                  // the number 6 is printed (0 + 1; 1 + 2; 3 + 3)

In this program fragment, the value of the variable i changes over time, taking the values 1, 2 and 3. This changing value—or mutable state—is characteristic of iteration.

Iteration can be approximated using recursive techniques in functional programming languages. The following example is in Scheme. Note that the following is recursive (a special case of iteration) because the definition of "how to iterate", the iter function, calls itself in order to solve the problem instance. Specifically it uses tail recursion so it does not use large amounts of stack space.

(let iterate ((i 1) (a 0))
  (if (<= i 3)
    (iterate (+ i 1) (+ a i))
    (display a)))

An iterator is an object that provides iteration as a generic service, allowing iteration to be done in the same way for a range of different data structures. Conversely, an iteratee is an abstraction which accepts or rejects data during an iteration process (controlled externally by an enumerator - so unlike with code that uses iterators, the iteratee code is not "in charge" of the iteration process).

Iteration is also performed using a worksheet, or by using solver or goal seek functions available in Excel. Many implicit equations like the Colebrook equation can be solved in the convenience of a worksheet by designing suitable calculation algorithms.^[3]

Many of the engineering problems like solving Colebrook equations reaches 8-digit accuracy in as small as 12 iterations and a maximum of 100 iterations is sufficient to reach a 15-digit accurate result.^[4]

Project management

Iterations in agile project management

Iterations in a project context may refer to the technique of developing and delivering incremental components of business functionality, product development or process design. This is most often associated with agile software development, but could potentially be any material. A single iteration results in one or more bite-sized but complete packages of project work that can perform some tangible business function. Multiple iterations recurse to create a fully integrated product. This is often contrasted with the waterfall model approach.^{[citation needed]}

Education

In some schools of pedagogy, iterations are used to describe the process of teaching or guiding students to repeat experiments, assessments, or projects, until more accurate results are found, or the student has mastered the technical skill. This idea is found in the old adage, "Practice makes perfect." In particular, "iterative" is defined as the "process of learning and development that involves cyclical inquiry, enabling multiple opportunities for people to revisit ideas and critically reflect on their implication."^[5]

References

^ B. Green (2012). Programming Problems. San Bernardino: CreateSpace. p. 25. ISBN 978-1475071962.
^ Eric Roberts (2006). Thinking Recursively with Java. New York: Wiley. p. 171. ISBN 978-0471701460.
^ "Solve Implicit Equations Inside Your Worksheet".
^ "Colebrook Equation".
^ Helen Timperley, Aaron Wilson, Heather Barrar, and Irene Fung. "Teacher Professional Learning and Development: Best Evidence Synthesis Iteration [BES]" (PDF). OECD. p. 238. Retrieved April 4, 2013.

External links

The dictionary definition of iteration at Wiktionary

UpToDate Contents

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English Journal

Multigrid solver for the reference interaction site model of molecular liquids theory.

Sergiievskyi VP, Hackbusch W, Fedorov MV.SourceMax Planck Institute of Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany.
Journal of computational chemistry.J Comput Chem.2011 Jul 15;32(9):1982-92. doi: 10.1002/jcc.21783. Epub 2011 Mar 31.
In this article, we propose a new multigrid-based algorithm for solving integral equations of the reference interactions site model (RISM). We also investigate the relationship between the parameters of the algorithm and the numerical accuracy of the hydration free energy calculations by RISM. For t
PMID 21455965

A methodology for automatic intensity-modulated radiation treatment planning for lung cancer.

Zhang X, Li X, Quan EM, Pan X, Li Y.AbstractIn intensity-modulated radiotherapy (IMRT), the quality of the treatment plan, which is highly dependent upon the treatment planner's level of experience, greatly affects the potential benefits of the radiotherapy (RT). Furthermore, the planning process is complicated and requires a great deal of iteration, and is often the most time-consuming aspect of the RT process. In this paper, we describe a methodology to automate the IMRT planning process in lung cancer cases, the goal being to improve the quality and consistency of treatment planning. This methodology (1) automatically sets beam angles based on a beam angle automation algorithm, (2) judiciously designs the planning structures, which were shown to be effective for all the lung cancer cases we studied, and (3) automatically adjusts the objectives of the objective function based on a parameter automation algorithm. We compared treatment plans created in this system (mdaccAutoPlan) based on the overall methodology with plans from a clinical trial of IMRT for lung cancer run at our institution. The 'autoplans' were consistently better, or no worse, than the plans produced by experienced medical dosimetrists in terms of tumor coverage and normal tissue sparing. We conclude that the mdaccAutoPlan system can potentially improve the quality and consistency of treatment planning for lung cancer.
Physics in medicine and biology.Phys Med Biol.2011 Jul 7;56(13):3873-93. Epub 2011 Jun 8.
In intensity-modulated radiotherapy (IMRT), the quality of the treatment plan, which is highly dependent upon the treatment planner's level of experience, greatly affects the potential benefits of the radiotherapy (RT). Furthermore, the planning process is complicated and requires a great deal of it
PMID 21654043

The performance of monotonic and new non-monotonic gradient ascent reconstruction algorithms for high-resolution neuroreceptor PET imaging.

Angelis GI, Reader AJ, Kotasidis FA, Lionheart WR, Matthews JC.SourceImaging, Proteomics and Genomics, MAHSC, University of Manchester, Wolfson Molecular Imaging Centre, Manchester, UK.
Physics in medicine and biology.Phys Med Biol.2011 Jul 7;56(13):3895-917. Epub 2011 Jun 8.
Iterative expectation maximization (EM) techniques have been extensively used to solve maximum likelihood (ML) problems in positron emission tomography (PET) image reconstruction. Although EM methods offer a robust approach to solving ML problems, they usually suffer from slow convergence rates. The
PMID 21654041

Japanese Journal

Minimization of the free energy under a given pressure by natural iteration method

Kiyokane Naoya,Mohri Tetsuo
Materials Transactions 52(3), 428-432, 2011-03
NAID 40018702961

Construction of Mutually Orthogonal Zero Correlation Zone Polyphase Sequence Sets

LI Yubo,XU Chengqian,LIU Kai
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94.A(4), 1159-1164, 2011
… The first one is based on DFT matrices and interleaving iteration. …
NAID 130000675280

Maxima Exploitation for Reference Blurring Function in Motion Deconvolution

CHONG Rachel Mabanag,TANAKA Toshihisa
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94.A(3), 921-928, 2011
… Its usage will result in a more stable learning and estimation process since it does not change with respect to iteration or any estimated value. …
NAID 130000675243