English Dictionary

Lipschitz condition

名詞

(mathematical analysis) A property which can be said to be held by some point in the domain of a real-valued function if there exists a neighborhood of that point and a certain constant such that for any other point in that neighborhood, the absolute value of the difference of their function values is less than the product of the constant and the absolute value of the difference between the two points.

日本語の意味

数学的解析における概念で、ある実数値関数が、特定の点の近傍内で、任意の2点間においてその関数値の差が、ある一定の正の定数と入力値の差の積よりも小さいという性質。すなわち、ある定数 L > 0 と、その点の近傍が存在し、任意の x, y に対して |f(x) - f(y)| ≤ L|x - y| が成立することを指す。

To ensure uniqueness of solutions to the differential equation, the textbook requires that the right-hand side satisfy the Lipschitz condition in a neighborhood of the initial value.

微分方程式の解の一意性を保証するために、教科書は右辺が初期値の近傍で、ある点の近傍に定数Lが存在し、その近傍内の任意の二点について関数値の差の絶対値が点の差の絶対値のL倍以下となるという性質（リプシッツ条件）を満たすことを要求している。

意味（1）

(mathematical analysis) A property which can be said to be held by some point in the domain of a real-valued function if there exists a neighborhood of that point and a certain constant such that for any other point in that neighborhood, the absolute value of the difference of their function values is less than the product of the constant and the absolute value of the difference between the two points.

Lipschitz conditions （ plural ）