How do you find the constant of a Lipschitz function?

How do you find the constant of a Lipschitz function?

  1. syms x.
  2. f = sin(x); % here we define the function.
  3. df = diff(f) % here we calculate the derivative function of sin(x)
  4. df = abs(df) % here we use the euclidean norm.
  5. fplot(df) % plots the abs(df). The function is clearly limited with upper bound M=1.
  6. % so the Lipschits constant is L >= 1.

Are constant functions Lipschitz?

Yes, for, if f is a constant function then every C>0 is such that |f(x)−f(y)|=0≤C|x−y| for all suitable x,y. Show activity on this post. Any L with |f(x)−f(y)|≤L|x−y| for all x,y is a Lipschitz constant for f. So if f is constant, any L≥0 is a Lipschitz constant.

Is Fxx a Lipschitz?

The function f(x) = |x| defined on the reals is Lipschitz continuous with the Lipschitz constant equal to 1, by the reverse triangle inequality. This is an example of a Lipschitz continuous function that is not differentiable.

What is Lipschitz norm?

The Lipschitz norm or Lipschitz modulus ‖f‖Lip of f:X→Y is the supremum of the absolute difference quotients. d(f(a),f(b))d(a,b) for a≠b in X. In general, this supremum is a lower real number; in particular, it may be infinite.

What does Lipschitz mean in German?

The name is derived from the Slavic “lipa,” meaning “linden tree” or “lime tree.” The name may relate to a number of different place names: “Liebeschitz,” the name of a town in Bohemia, “Leipzig,” the name of a famous German city, or “Leobschutz,” the name of a town in Upper Silesia.

How do I check my Lipschitz condition?

Let f(t, y) = ty2. Then since |f(t, y2) − f(t, y1)| = t|y2 + y1||y2 − y1| is not bounded by any constant times |y2 − y1|, f is not Lipschitz with respect to y on the domain R × R. However f is Lipschitz on any rectangle R = [a, b] × [c, d] since we have t|y1 + y2| ≤ 2 max{|a|, |b|} · max{|c|,|d|} on R.

What does the name Lipschitz mean?

What does Lifshitz mean?

Lifshitz (or Lifschitz) is a surname, which may be derived from the Polish city of Głubczyce (German: Leobschütz).

How common is name Lipschitz?

How Common Is The Last Name Lipschitz? This last name is the 306,186th most frequent surname world-wide, borne by approximately 1 in 5,900,847 people.

What kind of name is Lipschitz?

Lipschitz, Lipshitz, or Lipchitz is an Ashkenazi Jewish surname.

What does Lipschitz mean in English?

Lipschitzadjective. (Of a real-valued real function ) Such that there exists a constant such that whenever and are in the domain of , . Etymology: Named after Rudolf Lipschitz.

Is Lipschitz a real name?

Lipschitz, Lipshitz, or Lipchitz is an Ashkenazi Jewish surname. The surname has many variants, including: Lifshitz (Lifschitz), Lifshits, Lifshuts, Lefschetz; Lipschitz, Lipshitz, Lipshits, Lopshits, Lipschutz (Lipschütz), Lipshutz, Lüpschütz; Libschitz; Livshits; Lifszyc, Lipszyc.

What is Lipschitz method?

A method for testing diuretic activity in rats has been described by Lipschitz et al. (1943). The test is based on water and sodium excretion in test animals and compared to rats treated with a high dose of urea. The “Lipschitz-value” is the quotient between excretion by test animals and excretion by the urea control.

What does the surname Lipschitz mean?