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Difference between revisions of "Calculus of finite differences"
From Demopædia
(Eugen Grebenik et al., first edition 1958) |
(Eugen Grebenik et al., first edition 1958) |
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TofT|Lang=en|Ed=I|N=1|Color=yes|Te=graduation}}{{ | TofT|Lang=en|Ed=I|N=1|Color=yes|Te=graduation}}{{ | ||
TofT|Lang=en|Ed=I|N=1|SubN=2|Te=smoothing}}{{ | TofT|Lang=en|Ed=I|N=1|SubN=2|Te=smoothing}}{{ | ||
| − | TofT|Lang=ar|Ed=I|N=1|Te=تدريج بياني | + | TofT|Lang=ar|Ed=I|N=1|Te=تدريج بياني}}{{ |
| − | TofT|Lang=ar|Ed=I|N=1|SubN=2|Te=تمهيد | + | TofT|Lang=ar|Ed=I|N=1|SubN=2|Te=تمهيد}}{{ |
TofT|Lang=cs|Ed=I|N=1|Color=yes|Te=vyrovnání}}{{ | TofT|Lang=cs|Ed=I|N=1|Color=yes|Te=vyrovnání}}{{ | ||
TofT|Lang=de|Ed=I|N=1|Te=ausgeglichene Reihe}}{{ | TofT|Lang=de|Ed=I|N=1|Te=ausgeglichene Reihe}}{{ | ||
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{{NewLineT|S=151|N=2}} {{ | {{NewLineT|S=151|N=2}} {{ | ||
TofT|Lang=en|Ed=I|N=2|Color=yes|Te=graphic graduation}}{{ | TofT|Lang=en|Ed=I|N=2|Color=yes|Te=graphic graduation}}{{ | ||
| − | TofT|Lang=ar|Ed=I|N=2|Te=تمهيد بياني | + | TofT|Lang=ar|Ed=I|N=2|Te=تمهيد بياني}}{{ |
| − | TofT|Lang=ar|Ed=I|N=2|SubN=2|Te=تمهيد بياني | + | TofT|Lang=ar|Ed=I|N=2|SubN=2|Te=تمهيد بياني}}{{ |
| − | TofT|Lang=cs|Ed=I|N=2|Color=yes|Te= | + | TofT|Lang=cs|Ed=I|N=2|Color=yes|Te=grafické vyrovnání}}{{ |
TofT|Lang=de|Ed=I|N=2|Te=graphische Ausgleichung}}{{ | TofT|Lang=de|Ed=I|N=2|Te=graphische Ausgleichung}}{{ | ||
TofT|Lang=es|Ed=I|N=2|Color=yes|Te=ajuste gráfico}}{{ | TofT|Lang=es|Ed=I|N=2|Color=yes|Te=ajuste gráfico}}{{ | ||
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{{NewLineT|S=151|N=3}} {{ | {{NewLineT|S=151|N=3}} {{ | ||
TofT|Lang=en|Ed=I|N=3|Color=yes|Te=curve fitting}}{{ | TofT|Lang=en|Ed=I|N=3|Color=yes|Te=curve fitting}}{{ | ||
| − | TofT|Lang=ar|Ed=I|N=3|Te=توفيق المنحنيات | + | TofT|Lang=ar|Ed=I|N=3|Te=توفيق المنحنيات}}{{ |
| − | TofT|Lang=cs|Ed=I|N=3|Color=yes|Te= | + | TofT|Lang=cs|Ed=I|N=3|Color=yes|Te=analytické vyrovnání}}{{ |
TofT|Lang=de|Ed=I|N=3|Te=analytische Ausgleichung}}{{ | TofT|Lang=de|Ed=I|N=3|Te=analytische Ausgleichung}}{{ | ||
TofT|Lang=es|Ed=I|N=3|Color=yes|Te=analitico}}{{ | TofT|Lang=es|Ed=I|N=3|Color=yes|Te=analitico}}{{ | ||
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{{NewLineT|S=151|N=4}} {{ | {{NewLineT|S=151|N=4}} {{ | ||
TofT|Lang=en|Ed=I|N=4|Color=yes|Te=method of least squares}}{{ | TofT|Lang=en|Ed=I|N=4|Color=yes|Te=method of least squares}}{{ | ||
| − | TofT|Lang=ar|Ed=I|N=4|Te=طريقة المربعات الصغرى | + | TofT|Lang=ar|Ed=I|N=4|Te=طريقة المربعات الصغرى}}{{ |
TofT|Lang=cs|Ed=I|N=4|Color=yes|Te=metoda nejmenších čtverců}}{{ | TofT|Lang=cs|Ed=I|N=4|Color=yes|Te=metoda nejmenších čtverců}}{{ | ||
TofT|Lang=de|Ed=I|N=4|Te=Methode der kleinsten Quadrate}}{{ | TofT|Lang=de|Ed=I|N=4|Te=Methode der kleinsten Quadrate}}{{ | ||
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{{NewLineT|S=151|N=5}} {{ | {{NewLineT|S=151|N=5}} {{ | ||
TofT|Lang=en|Ed=I|N=5|Color=yes|Te=moving average}}{{ | TofT|Lang=en|Ed=I|N=5|Color=yes|Te=moving average}}{{ | ||
| − | TofT|Lang=ar|Ed=I|N=5|Te=متوسطات المتحركة | + | TofT|Lang=ar|Ed=I|N=5|Te=متوسطات المتحركة}}{{ |
TofT|Lang=cs|Ed=I|N=5|Color=yes|Te=metoda klouzavých průměrů}}{{ | TofT|Lang=cs|Ed=I|N=5|Color=yes|Te=metoda klouzavých průměrů}}{{ | ||
TofT|Lang=de|Ed=I|N=5|Te=Methode des gleitenden Durchschnitts}}{{ | TofT|Lang=de|Ed=I|N=5|Te=Methode des gleitenden Durchschnitts}}{{ | ||
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{{NewLineT|S=151|N=6}} {{ | {{NewLineT|S=151|N=6}} {{ | ||
TofT|Lang=en|Ed=I|N=6|Color=yes|Te=calculus of finite differences}}{{ | TofT|Lang=en|Ed=I|N=6|Color=yes|Te=calculus of finite differences}}{{ | ||
| − | TofT|Lang=ar|Ed=I|N=6|Te=حساب الفروق المحدودة | + | TofT|Lang=ar|Ed=I|N=6|Te=حساب الفروق المحدودة}}{{ |
TofT|Lang=cs|Ed=I|N=6|Color=yes|Te=diferenční metoda}}{{ | TofT|Lang=cs|Ed=I|N=6|Color=yes|Te=diferenční metoda}}{{ | ||
TofT|Lang=de|Ed=I|N=6|Te=Berechnung mit endlichen Differenzen}}{{ | TofT|Lang=de|Ed=I|N=6|Te=Berechnung mit endlichen Differenzen}}{{ | ||
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{{NewLineT|S=151|N=7}} {{ | {{NewLineT|S=151|N=7}} {{ | ||
TofT|Lang=en|Ed=I|N=7|Color=yes|Te=interpolation}}{{ | TofT|Lang=en|Ed=I|N=7|Color=yes|Te=interpolation}}{{ | ||
| − | TofT|Lang=ar|Ed=I|N=7|Te=استكمال | + | TofT|Lang=ar|Ed=I|N=7|Te=استكمال}}{{ |
TofT|Lang=cs|Ed=I|N=7|Color=yes|Te=interpolace}}{{ | TofT|Lang=cs|Ed=I|N=7|Color=yes|Te=interpolace}}{{ | ||
TofT|Lang=de|Ed=I|N=7|Te=Interpolation}}{{ | TofT|Lang=de|Ed=I|N=7|Te=Interpolation}}{{ | ||
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<noinclude> | <noinclude> | ||
| − | [[en-I:calculus of finite differences]] [[ar-I:حساب الفروق المحدودة | + | [[en-I:calculus of finite differences]] [[ar-I:حساب الفروق المحدودة]] [[cs-I:diferenční metoda]] [[de-I:Berechnung mit endlichen Differenzen]] [[es-I:diferencias finitas]] [[fi-I:differenssimenetelmä]] [[fr-I:calcul des différences finies]] [[it-I:calcolo delle differenze finite]] [[pl-I:rachunek różnic skończonych]] [[pt-I:CÁLCULO das diferenças finitas]] [[ru-I:Исчисление предельных отклонений]] |
</noinclude> | </noinclude> | ||
{{DEFAULTSORT:Calculus of finite differences}} | {{DEFAULTSORT:Calculus of finite differences}} | ||
Latest revision as of 07:19, 11 February 2010
| Translation | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Section | English 151 |
Arabic 151 |
Czech 151 |
German 151 |
Spanish 151 |
Finnish 151 |
French 151 |
Italien 151 |
[[pl-I:15#151|Template:Lang name -pl 151]] |
Portuguese 151 |
Russian 151 |
| 151-1 | graduation —smoothing |
تدريج بياني—تمهيد | vyrovnání | ausgeglichene Reihe —Ausgleichung |
ajustada —ajuste |
tasoittaminen | ajusté —ajustement —lissage |
perequazione —graduazione |
wartości wyrównane —wyrównywanie |
PEREQUAÇÃO —REGULARIZAÇÃO |
Выравнивание —Ряда сглаживание |
| 151-2 | graphic graduation | تمهيد بياني—تمهيد بياني | grafické vyrovnání | graphische Ausgleichung | ajuste gráfico | graafinen tasoittaminen | ajustement graphique | perequazione grafica | wyrównywanie graficzne | PEREQUAÇÃO gráfica | Графический метод выравнивания |
| 151-3 | curve fitting | توفيق المنحنيات | analytické vyrovnání | analytische Ausgleichung | analitico | analyyttinen tasoittaminen | ajustement analytique | perequazione analitica —interpolazione |
wyrównywanie analityczne | PEREQUAÇÃO analítica —AJUSTAMENTO de curva |
Аналитическое выравнивание |
| 151-4 | method of least squares | طريقة المربعات الصغرى | metoda nejmenších čtverců | Methode der kleinsten Quadrate | método de mínimos cuadrados | pienimmän neliösumman menetelmä | méthode des moindres carrés | metodo dei minimi quadrati | metoda najmniejszych kwadratów | MÉTODO dos mínimos quadrados | Способ наименьших квадратов |
| 151-5 | moving average | متوسطات المتحركة | metoda klouzavých průměrů | Methode des gleitenden Durchschnitts —Methode der gleitenden Durchschnitte |
medias móviles | liukuva keskiarvo | moyenne mobile | media mobile | średnia ruchoma | MÉDIA móvel | Скользящая средняя |
| 151-6 | calculus of finite differences | حساب الفروق المحدودة | diferenční metoda | Berechnung mit endlichen Differenzen —Differenzenmethode |
diferencias finitas | differenssimenetelmä | calcul des différences finies | calcolo delle differenze finite | rachunek różnic skończonych | CÁLCULO das diferenças finitas | Исчисление предельных отклонений |
| 151-7 | interpolation | استكمال | interpolace | Interpolation | interpolación | interpolointi | interpolation | interpolazione | interpolacja | INTERPOLAÇÃO | Интерполяция |
| 151-8 | extrapolation | استيفاء | extrapolace | Extrapolation | extrapolación | ekstrapolointi | extrapolation | estrapolazione —extrapolazione |
ekstrapolacja | EXTRAPOLAÇÃO | Экстраполяция |
It is occasionally desirable to replace a series of figures by another that shows greater regularity. This process is known as graduation1 or smoothing1, and it generally consists of passing a regular function through a number of points of the time series or other series, such as numbers of persons by reported ages. If a free-hand curve is drawn the process is known as graphic graduation2. Where analytical mathematical methods are used, this is called curve fitting3. A mathematical curve is fitted to the data, possibly by the method of least squares4, which minimizes the sum of the squares of the differences between the original and the graduated series. Other methods include moving averages5 or involve the use of the calculus of finite differences6. Some of the procedures may be used for interpolation7, the estimation of values of the series at points intermediate between given values or for extrapolation8, the estimation of values of the series outside the range for which it was given,
- 1. graduation n. — graduate v. — graduated adj. smoothing n. — smooth v. —smoothed adj.
- 7. interpolation n. — interpolate v. — interpolated adj.
- 8. extrapolation n. — extrapolate v. — extrapolated adj.
Audio pronunciation
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