WordNet
- wind around; move along a circular course; "round the bend"
- become round, plump, or shapely; "The young woman is fleshing out" (同)flesh out, fill out
- make round; "round the edges" (同)round_out, round_off
- the usual activities in your day; "the doctor made his rounds" (同)daily round
- a charge of ammunition for a single shot (同)unit of ammunition, one shot
- (often plural) a series of professional calls (usually in a set order); "the doctor goes on his rounds first thing every morning"; "the postmans rounds"; "we enjoyed our round of the local bars"
- a serving to each of a group (usually alcoholic); "he ordered a second round" (同)round of drinks
- a partsong in which voices follow each other; one voice starts and others join in one after another until all are singing different parts of the song at the same time; "they enjoyed singing rounds" (同)troll
- a cut of beef between the rump and the lower leg
- an outburst of applause; "there was a round of applause"
- the course along which communications spread; "the story is going the rounds in Washington"
- from beginning to end; throughout; "It rains all year round on Skye"; "frigid weather the year around" (同)around
- having a circular shape (同)circular
- pronounce with rounded lips (同)labialize, labialise
- (mathematics) expressed to the nearest integer, ten, hundred, or thousand; "in round numbers"
- not performing or scheduled for duties; "Hes off every Tuesday"
- at a distance in space or time; "the boat was 5 miles off (or away)"; "the party is still 2 weeks off (or away)"; "away back in the 18th century" (同)away
- (of events) no longer planned or scheduled; "the wedding is definitely off" (同)cancelled
- in an unpalatable state; "sour milk" (同)sour, turned
- below a satisfactory level; "an off year for tennis"; "his performance was off"
- no longer on or in contact or attached; "clean off the dirt"; "he shaved off his mustache"
- not in operation or operational; "the oven is off"; "the lights are off"
- the near or foreseeable future; "there was a wedding in the offing"
- the part of the sea that can be seen from the shore and is beyond the anchoring area; "there was a ship in the offing"
- (mathematics) a miscalculation that results from rounding off numbers to a convenient number of decimals; "the error in the calculation was attributable to rounding"; "taxes are rounded off to the nearest dollar but the rounding error is surprisingly small" (同)rounding error
PrepTutorEJDIC
- …『を[ぐるっと]回って』,を一周して / …『を曲がって』 / …『の周囲に』,を取り巻いて / …『のあちこちに』,の辺りに / …『ころ』 / (ぐるりと)回って,巡って / 周囲が(に) / あちこち[に],方々[に];行き渡って / 回り道して / (ある場所へ)回って / 『球状の』,丸い / (タイヤ・輪のように)円形の,丸い / (断面の丸い)円筒(円錐)形の / (肩・筆跡などが)丸みのある,丸々とした / 《名詞の前にのみ用いて》(数量が)完全の,ちょうどの / 『丸い物』;円,輪;球,円筒形 / (中心・軸をまわる)『回転』,(天体の)回転運動 / 《しばしば複数形で》(職務上などの)巡回,見回り / 《単数形で》(行い・でき事の一つの)連続;繰り返り;(…が)ひとしきり続くこと《+『of』+『名』》 / (ボクシングの一勝負の中の)『ラウンド』,回,(ゴルフデ全部のホールを回る)ラウンド,(カードゲームの)一回り / 輪唱 / (銃砲の)1回の射撃,一斉射撃 / (射撃用弾薬の)1回分 / (牛のもも肉の)丸切り,(パンの)丸切り《+『of』+『名』》 / 輪舞,円舞 / …‘を'『丸くする』,‘に'丸みをつける / …‘を'『回る』,曲がる / 〈端数をもつ数字〉‘を'端数を切り捨てて(概数で)表す《+『down』+『名』+『to』+『名』》 / …‘を'完成する,仕上げる / …‘を'くちびるを丸くして発音する / 『丸くなる』 / 回る,曲る / 完成する
- 《分離》(接触しているところ)『から』,から離れて,からはずれて / 《位置》…『から離れたところで』(『に』) / (本来の状態など)からはずれて,…が狂って,がなくなって / (本道など)からそれて,から横道にはいったところに / 《eat, dineなどと共に》…からとって[食べる] / 《『from off』の形で》《話》…から / (ある値段)から割り引いて / 《話》…をやめて,慎んで《+『名』(do『ing』)》 / (仕事義務など)から離れて,を休んで / (人)をたよって,にやっかいになって / (1)《運動・移動を表す動詞と共に》『離れて』,向こうへ / 《状態の動詞と共に》『離れて』 / 《瞬間の動作を表す動詞と共に》『離して』 / 『去って』,出かけて / (電気・ガス・水道などが)『切れて』 / (本来の位置・状態などから)『はずれて』 / (仕事・勤務などを)『旧んで』 / (時間的・空間的に)『離れて』 / 《動作の完了》『すっかり』,完全に / 割り引いて / (中心・的などから)『それた』,『離れた』,はずれた / 『時期はずれの』,(時期などが)いつもほどよくない,シーズン外の / (状態が)水準以下の,いつも調子(状態)でない / 《補語にのみ用いて》(予定・用意されたことが)取りやめになって / 《補語にのみ用いて》(電気器具などが)電源が切れて;(ガス・水道が)切れて,止まって / (人が)…の暮らしぶりで / 勤務のない,休みの / 取れて,ぬげて,はずれて / (馬・車の1対のうち)右側の / 《補語にのみ用いて》(走者が)すでに走り出して / 《おもに英》《補語にのみ用いて》(食物などが)いたんで食べられない;飲めない / 《英》《補語にのみ用いて》(食堂などでメニューには載っているが料理が)もう品切れで / 《英》《補語にのみ用いて》(人の態度が)誠意のない,不親切な,ひどい / 《名詞の前にのみ用いて》《the ~》(クリケットで)打者の右前方の
- 《所有・所属》…『の』,…のものである,…に属する・《材料・要素》…『でできた』,から成る・《部分》…『の』[『中の』] ・《数量・単位・種類を表す名詞に付いて》…の・《原因・動機》…『で』,のために(because of) ・《主格関係》…『の』,による,によって・《目的格関係》…『を』,の・《同格関係》…『という』・《関係・関連》…『についての』[『の』],の点で・《抽象名詞などと共に》…の[性質をもつ] ・《『It is』+『形』+『of』+『名』+『to』 doの形で,ofの後の名詞を意味上の主語として》・《分離》…『から』・《起原・出所》…『から』[『の』](out of) ・《『名』+『of』+『a』(『an』)+『名』の形で》…のような・《『名』+『of』+『mine』(『yours, his』など独立所有格)の形で》…の…・《時》(1)《副詞句を作って》…に《形容詞句を作って》…の・《時刻》《米》…前(to,《米》before)
- (陸から見える)沖,沖合い
Wikipedia preview
出典(authority):フリー百科事典『ウィキペディア(Wikipedia)』「2014/12/15 10:27:36」(JST)
[Wiki en表示]
For the acrobatic movement, roundoff, see Roundoff.
A round-off error,[1] also called rounding error,[2] is the difference between the calculated approximation of a number and its exact mathematical value. This is a form of quantization error.[3] One of the goals of numerical analysis is to estimate errors in calculations, including round-off error, when using approximation equations and/or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits).[4]
When a sequence of calculations subject to rounding error is made, errors may accumulate, sometimes dominating the calculation. In ill-conditioned problems, significant error may accumulate.[5]
Contents
- 1 Representation error
- 2 See also
- 3 References
- 4 External links
Representation error
The error introduced by attempting to represent a number using a finite string of digits is a form of round-off error called representation error.[6] Here are some examples of representation error in decimal representations:
Notation |
Representation |
Approximation |
Error |
1/7 |
0.142 857 |
0.142 857 |
0.000 000 142 857 |
ln 2 |
0.693 147 180 559 945 309 41... |
0.693 147 |
0.000 000 180 559 945 309 41... |
log10 2 |
0.301 029 995 663 981 195 21... |
0.3010 |
0.000 029 995 663 981 195 21... |
∛ 2 |
1.259 921 049 894 873 164 76... |
1.25992 |
0.000 001 049 894 873 164 76... |
√ 2 |
1.414 213 562 373 095 048 80... |
1.41421 |
0.000 003 562 373 095 048 80... |
e |
2.718 281 828 459 045 235 36... |
2.718 281 828 459 045 |
0.000 000 000 000 000 235 36... |
π |
3.141 592 653 589 793 238 46... |
3.141 592 653 589 793 |
0.000 000 000 000 000 238 46... |
Increasing the number of digits allowed in a representation reduces the magnitude of possible round-off errors, but any representation limited to finitely many digits will still cause some degree of round-off error for uncountably many real numbers. Additional digits used for intermediary steps of a calculation are known as guard digits.[7]
Rounding multiple times can cause error to accumulate.[8] For example, if 9.945309 is rounded to two decimal places (9.95), then rounded again to one decimal place (10.0), the total error is 0.054691. Rounding 9.945309 to one decimal place (9.9) in a single step introduces less error (0.045309). This commonly occurs when performing arithmetic operations (See Loss of Significance).
See also
- Precision (arithmetic)
- Truncation
- Rounding
- Loss of significance
- Floating point
- Kahan summation algorithm
- Machine epsilon
- Wilkinson's polynomial
References
- ^ Butt, Rizwan (2009), Introduction to Numerical Analysis Using MATLAB, Jones & Bartlett Learning, pp. 11–18, ISBN 9780763773762 .
- ^ Ueberhuber, Christoph W. (1997), Numerical Computation 1: Methods, Software, and Analysis, Springer, pp. 139–146, ISBN 9783540620587 .
- ^ Aksoy, Pelin; DeNardis, Laura (2007), Information Technology in Theory, Cengage Learning, p. 134, ISBN 9781423901402 .
- ^ Ralston, Anthony; Rabinowitz, Philip (2012), A First Course in Numerical Analysis, Dover Books on Mathematics (2nd ed.), Courier Dover Publications, pp. 2–4, ISBN 9780486140292 .
- ^ Chapman, Stephen (2012), MATLAB Programming with Applications for Engineers, Cengage Learning, p. 454, ISBN 9781285402796 .
- ^ Laplante, Philip A. (2000), Dictionary of Computer Science, Engineering and Technology, CRC Press, p. 420, ISBN 9780849326912 .
- ^ Higham, Nicholas J. (2002), Accuracy and Stability of Numerical Algorithms (2nd ed.), SIAM, pp. 43–44, ISBN 9780898715217 .
- ^ Volkov, E. A. (1990), Numerical Methods, Taylor & Francis, p. 24, ISBN 9781560320111 .
External links
- Roundoff Error at MathWorld.
- D. Goldberg, What Every Computer Scientist Should Know About Floating-Point Arithmetic
- 20 Famous Software Disasters
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Related Links
- round off 【句動】 丸みをつける ~の端数を切り捨てる、概数にする、四捨五入... - アルクがお届けする進化するオンライン英和・和英辞書データベース。一般的な単語や連語から、イディオム、専門用語、スラングまで幅広く収録。
- round off vb (tr, adverb) 1. (often foll by with) to bring to a satisfactory conclusion; complete, esp agreeably: we rounded off the evening with a brandy. 2. to make round or less jagged Thesaurus Antonyms Related Words Synonyms Legend:
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