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Old 2009-06-10, 12:29   #1
hallstei
 
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Default Lipschitz constants

Hi,

I believe this is the appropriate forum for asking this question, even though it is not homework per se.

Where do I find comprehensive information about how to (get my computer to) compute the Lipschitz constant for functions f(x,y)?

Cheers
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Old 2009-06-10, 12:49   #2
fivemack
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Isn't it just the maximum of the absolute value of the derivative?
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Old 2009-06-10, 14:05   #3
ATH
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http://mathworld.wolfram.com/LipschitzFunction.html

Its probably the constant C so |f(x)-f(y)| <= C * |x-y| for all x,y.

Yes, maximum |f´(x)| should be at least an upper bound for C.

Last fiddled with by ATH on 2009-06-10 at 14:11
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Old 2009-06-10, 19:26   #4
hallstei
 
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Quote:
Originally Posted by ATH View Post
http://mathworld.wolfram.com/LipschitzFunction.html

Its probably the constant C so |f(x)-f(y)| <= C * |x-y| for all x,y.

Yes, maximum |f´(x)| should be at least an upper bound for C.
Thanks, guys!

Was it really that simple!? I assumed the solution was far more complex, and have spent some time googling for really complicated words.

Any pointers to good textbooks that deals with how to automatically approximate maximums and minimums for general functions?

Cheers
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Old 2009-07-02, 20:56   #5
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Quote:
Originally Posted by hallstei View Post
Any pointers to good textbooks that deals with how to automatically approximate maximums and minimums for general functions?
Any Calculus book will do.
Generally, the extrema of a function g(x) occur when g'(x) changes sign (+ to - for maximum and - to + for minimum) which may take place when g'(x) = 0 or is undefined.
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