approximate

• v.

• 近似の、近くの、近づく

関

adjacent、approach、approximation、close、closely、near、nearby、proximity、vicinity

　 　 　 　 　

WordNet

1. very close in resemblance; "sketched in an approximate likeness"; "a near likeness" (同)near
2. not quite exact or correct; "the approximate time was 10 oclock"; "a rough guess"; "a ballpark estimate" (同)approximative, rough
3. located close together; "with heads close together"; "approximate leaves grow together but are not united" (同)close together
4. be close or similar; "Her results approximate my own" (同)come_close
5. used of hair or haircuts; "a close military haircut"
6. finish a game in baseball by protecting a lead; "The relief pitcher closed with two runs in the second inning"
7. inclined to secrecy or reticence about divulging information; "although they knew her whereabouts her friends kept close about it" (同)closelipped, closemouthed, secretive, tightlipped
8. in an attentive manner; "he remained close on his guard" (同)closely, tight
9. come together, as if in an embrace; "Her arms closed around her long lost relative" (同)come_together
10. crowded; "close quarters" (同)confining
11. marked by fidelity to an original; "a close translation"; "a faithful copy of the portrait"; "a faithful rendering of the observed facts" (同)faithful
12. fill or stop up; "Can you close the cracks with caulking?" (同)fill_up
13. become closed; "The windows closed with a loud bang" (同)shut
14. move so that an opening or passage is obstructed; make shut; "Close the door"; "shut the window" (同)shut
15. fitting closely but comfortably; "a close fit" (同)snug, close-fitting
16. (of a contest or contestants) evenly matched; "a close contest"; "a close election"; "a tight game" (同)tight
17. of textiles; "a close weave"; "smooth percale with a very tight weave" (同)tight
18. at or within a short distance in space or time or having elements near each other; "close to noon"; "how close are we to town?"; "a close formation of ships"
19. bar access to; "Due to the accident, the road had to be closed for several hours"
20. be priced or listed when trading stops; "The stock market closed high this Friday"; "My new stocks closed at $59 last night"
21. bring together all the elements or parts of; "Management closed ranks"
22. cause a window or an application to disappear on a computer desktop
23. change ones body stance so that the forward shoulder and foot are closer to the intended point of impact
24. close in relevance or relationship; "a close family"; "we are all...in close sympathy with..."; "close kin"; "a close resemblance"
25. complete a business deal, negotiation, or an agreement; "We closed on the house on Friday"; "They closed the deal on the building"
26. confined to specific persons; "a close secret"
27. draw near; "The probe closed with the space station"
28. engage at close quarters; "close with the enemy"
29. finish or terminate (meetings, speeches, etc.); "The meeting was closed with a charge by the chairman of the board"
30. rigorously attentive; strict and thorough; "close supervision"; "paid close attention"; "a close study"; "kept a close watch on expenditures"
31. strictly confined or guarded; "kept under close custody"
32. a relatively short golf shot intended to put the ball onto the putting green; "he lost the hole when his approach rolled over the green" (同)approach shot
33. the act of drawing spatially closer to something; "the hunters approach scattered the geese" (同)approaching, coming
34. the temporal property of becoming nearer in time; "the approach of winter" (同)approaching, coming
35. ideas or actions intended to deal with a problem or situation; "his approach to every problem is to draw up a list of pros and cons"; "an attack on inflation"; "his plan of attack was misguided" (同)attack, plan of attack
36. a close approximation; "the nearest approach to genius"
37. make advances to someone, usually with a proposal or suggestion; "I was approached by the President to serve as his adviser in foreign matters"
38. the event of one object coming closer to another (同)approaching
39. come near in time; "Winter is approaching"; "approaching old age" (同)come_near
40. move towards; "We were approaching our destination"; "They are drawing near"; "The enemy army came nearer and nearer" (同)near, come_on, go_up, draw near, draw_close, come_near
41. closely resembling the genuine article; "near beer"; "a dress of near satin"
42. not far distant in time or space or degree or circumstances; "near neighbors"; "in the near future"; "they are near equals"; "his nearest approach to success"; "a very near thing"; "a near hit by the bomb"; "she was near tears"; "she was close to tears"; "had a close call" (同)close, nigh
43. being on the left side; "the near or nigh horse is the one on the left"; "the animals left side is its near or nigh side" (同)nigh
44. near in time or place or relationship; "as the wedding day drew near"; "stood near the door"; "dont shoot until they come near"; "getting near to the true explanation"; "her mother is always near"; "The end draws nigh"; "the bullet didnt come close"; "dont get too close to the fire" (同)nigh, close
45. near or close to but not necessarily touching; "lands adjacent to the mountains"; "New York and adjacent cities"
46. having a common boundary or edge; abutting; touching; "Rhode Island has two bordering states; Massachusetts and Conncecticut"; "the side of Germany conterminous with France"; "Utah and the contiguous state of Idaho"; "neighboring cities" (同)conterminous, contiguous, neighboring
47. nearest in space or position; immediately adjoining without intervening space; "had adjacent rooms"; "in the next room"; "the person sitting next to me"; "our rooms were side by side" (同)next, side_by_side
48. in a close relation or position in time or space; "the onsets were closely timed"; "houses set closely together"; "was closely involved in monitoring daily progress"
49. in a close manner; "the two phenomena are intimately connected"; "the person most nearly concerned" (同)intimately, nearly
50. (of quantities) imprecise but fairly close to correct; "lasted approximately an hour"; "in just about a minute"; "hes about 30 years old"; "Ive had about all I can stand"; "we meet about once a month"; "some forty people came"; "weighs around a hundred pounds"; "roughly $3,000"; "holds 3 gallons, more or less"; "20 or so people were at the party" (同)about, close_to, just about, some, roughly, more or less, around, or so
51. near to the scope or range of something; "his answer wasnt even in the right ballpark" (同)ballpark

PrepTutorEJDIC

1. (数量の点で)『近似の』・おおよその / 《『approximate to』+『名』》(…に)『近い』,ほぼ等しい / (ある状態・量・額などの点で)…‘に'『近づく』,接近する / (…の額に)…'を'概算する,見積もる《+『名』+『at』+『名』》
2. …'を'『閉じる』,閉める(shut) / …'を'ふさぐ(fill) / 〈事務・仕事・話など〉'を'『終える』,済ませる / 〈通路・施設など〉'を'一時的に閉じる,‘の'使用を一時中止する / (一つにまとまるように)…'を'つめる / 〈ドア・目・花などが〉『閉じる』,閉まる;ふさがる / 〈話・相談・契約などが〉『終る』,終了する,〈店などが〉終業(休業)する / くっつく,接近する(come together) / 終結,結末,終り(end) / 締め切り / (音楽の)終止
3. (距離・時間・関係が)『近い』,接近している・《名詞の前にのみ用いて》『親密な』,親しい・ぎっしり詰まった,密集した;目のつんだ,きめの細かい・綿密な,厳重な(strict) ・息がつまる,重苦しい(stuffy) / 厳重に隠された,秘密の / ほとんど同等の,匹敵する・《補語にのみ用いて》(金銭が)乏しい;(…に)けちな(stingy)《+『with』+『名』》・(音声が)閉鎖音の(舌を口蓋(こうがい)に近づけて発音する) / (…に)『近接して』,(…の)すぐそば(近く)に;(…に)ぴったりくっついて《+『to(behind, by)』+『名』》 / きっちりと;ぎっしりと・(大寺院の)囲い地;(学校の)構内,校庭・《英》袋小路
4. 〈ある時間・場所・状態〉‘に'『近づく』,接近する / (ある目的・要求で)〈人〉‘に'近づく,交渉する《+『名』〈人〉+『on』(『about』)+『名』(do『ing』)》 / 〈研究・仕事など〉‘に'取りかかる,〈問題など〉'を'扱う / 〈時・事などが〉『近づく』 / (程度・性質などにおいて)(…に)似ている,近い《+『to』+『名』》 / 〈U〉〈C〉(…に)『接近』,近づくこと《+『to』+『名』》 / 《しばしば複数形で》(ある目的で)(人に)近づくこと,取り入ること《+『to』+『名』》 / 〈U〉(…との)近似,類似《+『to』+『名』》 / 〈C〉(…へ)近づく道,(…への)入り口《+『to』+『名』》 / 〈C〉(問題・作品などの)扱い方,手引き;(…の)学習(研究)法《+『to』+『名』》
5. (空間的・時間的に)(…の)『近くに』,(…に)接近して《+『to』+『名』》 / 《しばしば複合語を作って》『ほとんど』(almost, nearly) / (空間的・時間的に)『近い』,接近した / (関係などが)『身近な』 / 『きわどい』,やっとの / (空間的・時間的に)…『に近く』,『の近くに』 / (状態などが)…に近く,…しそうで / (時間・空間上)…‘に'近づく / 近づく,接近する
6. 「ほとんど…,ほぼ…」の意を表す
7. 《文》近接の,隣接している;(…に)すぐ近くの《+『to』+『名』》
8. 『ぴったりと』,きっちりと / 『詳しく』,精密に / 近く,接近して / 密接に,仲よく / ひそかに,内密に
9. おおよそ,だいたい(nearly)

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/07/19 22:34:44」(JST)

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Part of a series on
Certainty
Agnosticism Approximation Belief Certainty Doubt Determinism Epistemology Fallibilism Fatalism Hypothesis Justification Nihilism Probability Scientific theory Skepticism Solipsism Theory Truth Uncertainty

For the sound change, see Lenition.

An approximation is anything that is similar but not exactly equal to something else. The term can be applied to various properties (e.g. value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g. the approximate time was 10 o'clock).

Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.

In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. An approximate model is used to make calculations easier. Approximations might also be used if incomplete information prevents use of exact representations.

The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation.

Mathematics

Approximation theory is a branch of mathematics, a quantitative part of functional analysis. Diophantine approximation deals with approximations of real numbers by rational numbers. Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain. However some known form may exist and may be able to represent the real form so that no significant deviation can be found. It also is used when a number is not rational, such as the number π, which often is shortened to 3.14159, or √2 to 1.414.

Numerical approximations sometimes result from using a small number of significant digits. Calculations are likely to involve rounding errors leading to approximation. Log tables, slide rules and calculators produce approximate answers to all but the simplest calculations. The results of computer calculations are normally an approximation expressed in a limited number of significant digits, although they can be programmed to produce more precise results. Approximation can occur when a decimal number cannot be expressed in a finite number of binary digits.

Related to approximation of functions is the asymptotic value of a function, i.e. the value as one or more of a function's parameters becomes arbitrarily large. For example, the sum (k/2)+(k/4)+(k/8)+...(k/2^n) is asymptotically equal to k. Unfortunately no consistent notation is used throughout mathematics and some texts will use ≈ to mean approximately equal and ~ to mean asymptotically equal whereas other texts use the symbols the other way around.

As another example, in order to accelerate the convergence rate of evolutionary algorithms, fitness approximation—that leads to build model of the fitness function to choose smart search steps—is a good solution.

Science

Approximation arises naturally in scientific experiments. The predictions of a scientific theory can differ from actual measurements. This can be because there are factors in the real situation that are not included in the theory. For example simple calculations may not include the effect of air resistance. Under these circumstances, the theory is an approximation to reality. Differences may also arise because of limitations in the measuring technique. In this case, the measurement is an approximation to the actual value.

The history of science shows that earlier theories and laws can be approximations to some deeper set of laws. Under the correspondence principle, a new scientific theory should reproduce the results of older, well-established, theories in those domains where the old theories work. The old theory becomes an approximation to the new theory.

Some problems in physics are too complex to solve by direct analysis, or progress could be limited by available analytical tools. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly. Physicists often approximate the shape of the Earth as a sphere even though more accurate representations are possible, because many physical characteristics (e.g. gravity) are much easier to calculate for a sphere than for other shapes.

Approximation is also used to analyze the motion of several planets orbiting a star. This is extremely difficult due to the complex interactions of the planets' gravitational effects on each other. An approximate solution is effected by performing iterations. In the first iteration, the planets' gravitational interactions are ignored, and the star is assumed to be fixed. If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others. This process may be repeated until a satisfactorily precise solution is obtained.

The use of perturbations to correct for the errors can yield more accurate solutions. Simulations of the motions of the planets and the star also yields more accurate solutions.

The most common versions of philosophy of science accept that empirical measurements are always approximations—they do not perfectly represent what is being measured.

Unicode

See also: Unicode mathematical operators

Symbols representing approximation:

≐	general approximation
≈	asymptotic analysis

Symbols used to denote items that are approximately equal are wavy or dotted equals signs.

• ≈ (U+2248)
• ≃ (U+2243), a combination of "≈" and "=", also used to indicate asymptotically equal to
• ≅ (U+2245), another combination of "≈" and "=", which is used to indicate isomorphism or sometimes congruence
• ≊ (U+224A), also a combination of "≈" and "=", used to indicate equivalence or approximate equivalence
• ∼ (U+223C), which is also sometimes used to indicate proportionality
• ∽ (U+223D), which is also sometimes used to indicate proportionality
• ≐ (U+2250), which can also be used to represent the approach of a variable to a limit
• ≒ (U+2252), which is used like "≃" in both Japanese and Korean
• ≓ (U+2253), a reversed variation of "≒"

LaTeX Symbols

(\approx), usually to indicate approximation between numbers, like .

(\simeq), usually to indicate asymptotic equivalence between functions, like . So writing would be wrong, despite wide use.

(\sim), usually to indicate proportionality between functions, the same of the line above will be .

(\cong), usually to indicate congruence between figures, like .

See also

• Approximately equals sign
• Approximation error
• Congruence relation
• Estimation
• Fermi estimate
• Fitness approximation
• Least squares
• Linear approximation
• Newton's method
• Numerical analysis
• Orders of approximation
• Runge–Kutta methods
• Successive approximation ADC
• Taylor series

References

External links

UpToDate Contents

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English Journal

• Dynamic semiparametric Bayesian models for genetic mapping of complex trait with irregular longitudinal data.

• Das K, Li J, Fu G, Wang Z, Li R, Wu R.SourceCenter for Statistical Genetics, The Pennsylvania State University, Hershey, PA, 17033, U.S.A.; Department of Statistics, The Pennsylvania State University, University Park, PA, 16802, U.S.A.
• Statistics in medicine.Stat Med.2013 Feb 10;32(3):509-23. doi: 10.1002/sim.5535. Epub 2012 Aug 17.
• Many phenomena of fundamental importance to biology and biomedicine arise as a dynamic curve, such as organ growth and HIV dynamics. The genetic mapping of these traits is challenged by longitudinal variables measured at irregular and possibly subject-specific time points, in which case nonnegative
• PMID 22903809

• Cusp radius measurement through digital image analysis.

• Frunza MC, Suciu C.SourceUniversity of Medicine and Pharmacy, Faculty of Dental Medicine , Bucharest , Romania.
• Acta odontologica Scandinavica.Acta Odontol Scand.2013 Feb;71(1):236-40. doi: 10.3109/00016357.2012.671359. Epub 2012 Mar 20.
• Abstract Objective. Dental anatomy has been extensively described in numerous textbooks. Nevertheless, there are very few details about the value of the cusp radius of posterior teeth. This in vitro study used a laser profilometer to scan the occlusal surfaces of 21 molar teeth. Materials and
• PMID 22428903

• Stroke survivors control the temporal structure of variability during reaching in dynamic environments.

• Mukherjee M, Koutakis P, Siu KC, Fayad PB, Stergiou N.SourceNebraska Biomechanics Core Facility, University of Nebraska at Omaha, Omaha, NE, 68182-0216, USA.
• Annals of biomedical engineering.Ann Biomed Eng.2013 Feb;41(2):366-76. doi: 10.1007/s10439-012-0670-9. Epub 2012 Oct 13.
• Learning to control forces is known to reduce the amount of movement variability (e.g., standard deviation; SD) while also altering the temporal structure of movement variability (e.g., approximate entropy; ApEn). Such variability control has not been explored in stroke survivors during reaching mov
• PMID 23064865

• The appropriate use of approximate entropy and sample entropy with short data sets.

• Yentes JM, Hunt N, Schmid KK, Kaipust JP, McGrath D, Stergiou N.SourceNebraska Biomechanics Core Facility, Department of Health, Physical Education, and Recreation, University of Nebraska at Omaha, 6001 Dodge Street, HPER 207, Omaha, NE, 68182, USA.
• Annals of biomedical engineering.Ann Biomed Eng.2013 Feb;41(2):349-65. doi: 10.1007/s10439-012-0668-3. Epub 2012 Oct 12.
• Approximate entropy (ApEn) and sample entropy (SampEn) are mathematical algorithms created to measure the repeatability or predictability within a time series. Both algorithms are extremely sensitive to their input parameters: m (length of the data segment being compared), r (similarity criterion),
• PMID 23064819

Japanese Journal

• Effectiveness of Approximation Strategy in Surrogateassisted Fireworks Algorithm

• Pei Yan,Zheng Shaoqiu,Tan Ying,Takagi Hideyuki
• International Journal of Machine Learning and Cybernetics 2015(7), 2015-07-14
• … We investigate the effectiveness of approximation strategy in a surrogate-assisted fireworks algorithm, which obtains the elite from approximate fitness landscape to enhance its optimization performance. … For the approximation method, we use least square approximation, spline interpolation, Newton interpolation, and support vector regression to approximate fitness landscape of fireworks algorithm in projected lower dimensional, original and higher dimensional search space. …
• NAID 120005624070

• 三次元空間における効率良い近似点集合マッチングと分子パターン照合への応用 (情報論的学習理論と機械学習)

• 佐々木 耀一,渋谷 哲朗,伊藤 公人 [他]
• 電子情報通信学会技術研究報告 = IEICE technical report : 信学技報 115(112), 335-341, 2015-06-23
• NAID 40020525492

• 三次元空間における効率良い近似点集合マッチングと分子パターン照合への応用 (ニューロコンピューティング)

• 佐々木 耀一,渋谷 哲朗,伊藤 公人 [他]
• 電子情報通信学会技術研究報告 = IEICE technical report : 信学技報 115(111), 219-225, 2015-06-23
• NAID 40020524990

• トラジェクトリデータに対する効率良い近似パターン照合アルゴリズム (コンピュテーション)

• 笹川 裕人,有村 博紀
• 電子情報通信学会技術研究報告 = IEICE technical report : 信学技報 115(84), 133-139, 2015-06-12
• NAID 40020523941

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★リンクテーブル★

リンク元	「close」「adjacent」「近く」「closely」「near」
拡張検索	「approximately」

「close」

　　[★]

• adj.

• 近くの、近接する、密接な、閉じる、閉鎖する、終える

関

adjacent、approximate、atresia、closely、closure、contiguous、inextricably、intimate、near、nearby、occlude、occlusion、proximate、proximity、shut、terminate、tight、tighten、tightly、vicinal、vicinity

　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　

「adjacent」

　　[★]

• 隣接性の、隣接する、隣接的な、近接する、近くの

関

abut、adjacently、anchimeric、approximate、close、closely、contiguous、flank、flanking、near、nearby、neighboring、neighbouring、proximate、proximity、vicinal、vicinity

　 　 　 　

「近く」

　　[★]

英

proximity、vicinity、adjacent、close、approximate、nearby、closely、near

関

近似、近接、近傍、閉じる、閉鎖、隣接、隣接性、隣接的、終える、接近して、密接、近づく、付近

「closely」

　　[★]

• adv.

• 密接に、接近して、近くに

関

adjacent、approximate、close、inextricably、intimate、near、nearby、proximity、tight、tighten、tightly、vicinity

　 　 　

「near」

　　[★]

• adv. prep.

• 付近に、近くに

関

adjacent、approximate、close、closely、nearby、neighboring、proximity、vicinity

　 　 　 　 　 　

「approximately」

　　[★]

• 約、およそ

関

a matter of、about、approx.、around、ca.、circa、roughly