English Dictionary

Gibbs phenomenon

固有名詞

(mathematics) A behaviour of the Fourier series approximation at a jump discontinuity of a piecewise continuously differentiable periodic function, such that partial sums exhibit an oscillation peak adjacent the discontinuity that may overshoot the function maximum (or minimum) itself and does not disappear as more terms are calculated, but rather approaches a finite limit.

日本語の意味

（数学）フーリエ級数による近似において、区分的に連続微分可能な周期関数の跳躍不連続点周辺で、部分和が振動し、跳躍点付近に顕著なピーク（関数の最大値または最小値を超える可能性がある）が現れる現象で、このピークは項数が増加しても解消されず、有限の極限値に収束する挙動を指す

When approximating a square wave with its Fourier series, the Gibbs phenomenon produces persistent oscillation peaks near each jump discontinuity that do not disappear as more terms are added.

方形波をフーリエ級数で近似すると、ギブズ現象により各不連続点付近に残留する振動のピークが現れ、項を増やしても消えず有限の値に近づきます。

意味（1）

(mathematics) A behaviour of the Fourier series approximation at a jump discontinuity of a piecewise continuously differentiable periodic function, such that partial sums exhibit an oscillation peak adjacent the discontinuity that may overshoot the function maximum (or minimum) itself and does not disappear as more terms are calculated, but rather approaches a finite limit.

The Gibbs phenomenon is characteristic of Fourier series at a discontinuity, its size being proportional to the magnitude of the discontinuity.