Rate of convergence (original) (raw)
En càlcul numèric la velocitat amb la qual una successió convergeix al seu límit s'anomena ordre de convergència. Aquest concepte és, des del punt de vista pràctic, molt important si necessitem treballar amb seqüències de successives aproximacions d'un mètode iteratiu. Fins i tot pot marcar la diferència entre necessitar deu o un milió d'iteracions.
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| dbo:abstract | En càlcul numèric la velocitat amb la qual una successió convergeix al seu límit s'anomena ordre de convergència. Aquest concepte és, des del punt de vista pràctic, molt important si necessitem treballar amb seqüències de successives aproximacions d'un mètode iteratiu. Fins i tot pot marcar la diferència entre necessitar deu o un milió d'iteracions. (ca) في التحليل العددي، السرعة التي تقترب بها متتالية متقاربة ما من نهايتها تسمى سرعة التقارب (بالإنجليزية: Rate of convergence). (ar) Unter Konvergenzgeschwindigkeit (auch Konvergenzordnung) versteht man die Geschwindigkeit, mit der sich die Glieder einer konvergenten Folge dem Grenzwert nähern. In der numerischen Mathematik ist die Konvergenzgeschwindigkeit ein wichtiges Qualitätsmerkmal iterativer Verfahren, neben dem Rechenaufwand pro Iteration und der numerischen Stabilität. (de) En analyse numérique — une branche des mathématiques — on peut classer les suites convergentes en fonction de leur vitesse de convergence vers leur point limite. C'est une manière d'apprécier l'efficacité des algorithmes qui les génèrent. Les suites considérées ici sont convergentes sans être stationnaires (tous leurs termes sont même supposés différents du point limite). Si une suite est stationnaire, tous ses éléments sont égaux à partir d'un certain rang et il est alors normal de s'intéresser au nombre d'éléments différents du point limite. C'est ce que l'on fait lorsqu'on étudie la complexité des algorithmes trouvant ce qu'ils cherchent en un nombre fini d'étapes. (fr) En análisis numérico la velocidad con la cual una sucesión converge a su límite es llamada orden de convergencia. Este concepto es, desde el punto de vista práctico, muy importante si necesitamos trabajar con secuencias de sucesivas aproximaciones de un método iterativo. Incluso puede hacer la diferencia entre necesitar diez o un millón de iteraciones. (es) In numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence that converges to is said to have order of convergence and rate of convergence if The rate of convergence is also called the asymptotic error constant.Note that this terminology is not standardized and some authors will use rate wherethis article uses order (e.g., ). In practice, the rate and order of convergence provide useful insights when using iterative methods for calculating numerical approximations. If the order of convergence is higher, then typically fewer iterations are necessary to yield a useful approximation. Strictly speaking, however, the asymptotic behavior of a sequence does not give conclusive information about any finite part of the sequence. Similar concepts are used for discretization methods. The solution of the discretized problem converges to the solution of the continuous problem as the grid size goes to zero, and the speed of convergence is one of the factors of the efficiency of the method. However, the terminology, in this case, is different from the terminology for iterative methods. Series acceleration is a collection of techniques for improving the rate of convergence of a series discretization. Such acceleration is commonly accomplished with sequence transformations. (en) Em análise numérica, a velocidade com que uma série convergente se aproxima do seu limite é chamada de taxa de convergência. Embora estritamente falando, o comportamento assintótico de uma sequência não forneça informações sobre qualquer primeira parte finita desta, este conceito é de importância prática se lidamos com uma sequência de sucessivas aproximações para um método iterativo, assim, poucas iterações são necessárias para se obter uma boa aproximação quando a taxa de convergência é alta. Isso pode até mesmo fazer a diferença entre necessitar dez ou um milhão de iterações. Conceitos semelhantes são usados para métodos discretos. A solução de um problema discreto converge para a solução de um problema contínuo quando o tamanho da grade tende a zero, e a velocidade da convergência é um dos fatores de eficiência do método. No entanto, a terminologia, nesse caso, é diferente da terminologia para métodos iterativos. (pt) Швидкість збіжності є основною характеристикою чисельних методів розв'язування рівнянь і оптимізації. (uk) Скорость сходимости является основной характеристикой численных методов решения уравнений и оптимизации. (ru) 在數值分析中, 一個收斂序列向其極限逼近的速度稱為收斂速度. 該概念多用於最優化算法中; 其被定義為一個疊代序列向其局部最優值逼近 (假設計算過程收斂, 並能逹到最優值) 的速度, 是評價一個疊代法於該問題中發揮的性能的一個重要指標. (zh) |
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| dbp:date | August 2020 (en) |
| dbp:reason | There appears to be a mixture of defining convergence with regards to grid points and with step size . Section should be modified for consistency and include an explanation of alternative definitions. (en) |
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| rdfs:comment | En càlcul numèric la velocitat amb la qual una successió convergeix al seu límit s'anomena ordre de convergència. Aquest concepte és, des del punt de vista pràctic, molt important si necessitem treballar amb seqüències de successives aproximacions d'un mètode iteratiu. Fins i tot pot marcar la diferència entre necessitar deu o un milió d'iteracions. (ca) في التحليل العددي، السرعة التي تقترب بها متتالية متقاربة ما من نهايتها تسمى سرعة التقارب (بالإنجليزية: Rate of convergence). (ar) Unter Konvergenzgeschwindigkeit (auch Konvergenzordnung) versteht man die Geschwindigkeit, mit der sich die Glieder einer konvergenten Folge dem Grenzwert nähern. In der numerischen Mathematik ist die Konvergenzgeschwindigkeit ein wichtiges Qualitätsmerkmal iterativer Verfahren, neben dem Rechenaufwand pro Iteration und der numerischen Stabilität. (de) En análisis numérico la velocidad con la cual una sucesión converge a su límite es llamada orden de convergencia. Este concepto es, desde el punto de vista práctico, muy importante si necesitamos trabajar con secuencias de sucesivas aproximaciones de un método iterativo. Incluso puede hacer la diferencia entre necesitar diez o un millón de iteraciones. (es) Швидкість збіжності є основною характеристикою чисельних методів розв'язування рівнянь і оптимізації. (uk) Скорость сходимости является основной характеристикой численных методов решения уравнений и оптимизации. (ru) 在數值分析中, 一個收斂序列向其極限逼近的速度稱為收斂速度. 該概念多用於最優化算法中; 其被定義為一個疊代序列向其局部最優值逼近 (假設計算過程收斂, 並能逹到最優值) 的速度, 是評價一個疊代法於該問題中發揮的性能的一個重要指標. (zh) In numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence that converges to is said to have order of convergence and rate of convergence if The rate of convergence is also called the asymptotic error constant.Note that this terminology is not standardized and some authors will use rate wherethis article uses order (e.g., ). (en) En analyse numérique — une branche des mathématiques — on peut classer les suites convergentes en fonction de leur vitesse de convergence vers leur point limite. C'est une manière d'apprécier l'efficacité des algorithmes qui les génèrent. (fr) Em análise numérica, a velocidade com que uma série convergente se aproxima do seu limite é chamada de taxa de convergência. Embora estritamente falando, o comportamento assintótico de uma sequência não forneça informações sobre qualquer primeira parte finita desta, este conceito é de importância prática se lidamos com uma sequência de sucessivas aproximações para um método iterativo, assim, poucas iterações são necessárias para se obter uma boa aproximação quando a taxa de convergência é alta. Isso pode até mesmo fazer a diferença entre necessitar dez ou um milhão de iterações. (pt) |
| rdfs:label | سرعة التقارب (ar) Taxa de convergència (ca) Konvergenzgeschwindigkeit (de) Orden de convergencia (es) Laju konvergensi (in) Vitesse de convergence des suites (fr) Rate of convergence (en) Taxa de convergência (pt) Скорость сходимости (ru) 收斂速度 (zh) Швидкість збіжності (uk) |
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