Enter the maximum difference of the function values and the maximum difference of the inputs into the calculator to determine the Lipschitz constant for a function on a given interval.
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Lipschitz Constant Formula
The following formula is used to calculate the Lipschitz constant.
L = |f(x1) - f(x2)| / |x1 - x2|
Variables:
- L is the Lipschitz constant
- |f(x1) – f(x2)| is the maximum difference of the function values on the interval
- |x1 – x2| is the maximum difference of the inputs on the interval
To calculate the Lipschitz constant, divide the maximum difference of the function values by the maximum difference of the inputs on the interval.
What is a Lipschitz Constant?
The Lipschitz constant is a measure of how much a function can stretch or compress values between two points. It is a crucial concept in mathematical analysis, particularly in the study of differential equations and optimization problems. A function is said to be Lipschitz continuous if there exists a real number L, known as the Lipschitz constant, such that for every pair of points within the domain, the absolute difference between the function values is at most L times the absolute difference between the points.
How to Calculate Lipschitz Constant?
The following steps outline how to calculate the Lipschitz Constant.
- First, determine the maximum difference of the function values (|f(x1) – f(x2)|).
- Next, determine the maximum difference of the inputs (|x1 – x2|).
- Use the formula L = |f(x1) – f(x2)| / |x1 – x2| to calculate the Lipschitz constant (L).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Maximum difference of the function values (|f(x1) – f(x2)|) = 8
Maximum difference of the inputs (|x1 – x2|) = 2
