Runge's phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl David Tolmé Runge (1901) when exploring the behavior of errors when using polynomial interpolation to approximate certain functions.The discovery was important because it shows that going to higher degrees does not always improve accuracy. The phenomenon is similar to the Gibbs phenomenon in Fourier series approximations.
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Runge's phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl David Tolmé Runge (1901) when exploring the behavior of errors when using polynomial interpolation to approximate certain functions.The discovery was important because it shows that going to higher degrees does not always improve accuracy. The phenomenon is similar to the Gibbs phenomenon in Fourier series approximations.
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Dans le domaine mathématique d ...... augmente indéfiniment avec n.
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Efekt Rungego (od nazwiska Car ...... anu Czebyszewa n-tego stopnia.
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Em matemática, em particular n ...... ximações em séries de Fourier.
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En el campo matemático del aná ...... oximar determinadas funciones.
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In Analisi numerica il Fenomen ...... approssimare alcune funzioni.
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In the mathematical field of n ...... Fourier series approximations.
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Феномен (явление) Рунге — в чи ...... а может быть точка экстремума.
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ルンゲ現象（英: Runge's phenomenon）は、 ...... る関数を多項式補間で近似したときの誤差を調べていて発見した。
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在数值分析领域中， 龙格现象是用高阶多项式进行多项式插值时所出现的问题。它是 Carle David Tolmé Runge 在研究使用多项式插值逼近特定函数的误差过程中发现的。
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Dans le domaine mathématique d ...... augmente indéfiniment avec n.
@fr
Efekt Rungego (od nazwiska Car ...... znacząco od funkcji gładkiej.
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Em matemática, em particular n ...... ximações em séries de Fourier.
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En el campo matemático del aná ...... oximar determinadas funciones.
@es
In Analisi numerica il Fenomen ...... approssimare alcune funzioni.
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In the mathematical field of n ...... Fourier series approximations.
@en
Феномен (явление) Рунге — в чи ...... и ограничена точка экстремума.
@ru
ルンゲ現象（英: Runge's phenomenon）は、 ...... る関数を多項式補間で近似したときの誤差を調べていて発見した。
@ja
在数值分析领域中， 龙格现象是用高阶多项式进行多项式插值时所出现的问题。它是 Carle David Tolmé Runge 在研究使用多项式插值逼近特定函数的误差过程中发现的。
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Efekt Rungego
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Fenomeno di Runge
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Fenómeno de Runge
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Fenómeno de Runge
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Phénomène de Runge
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Runge's phenomenon
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Феномен Рунге
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ルンゲ現象
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龙格现象
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