mersenneforum.org Lipschitz constants
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 2009-06-10, 12:29 #1 hallstei     Apr 2005 11012 Posts 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
 2009-06-10, 12:49 #2 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 2×7×461 Posts Isn't it just the maximum of the absolute value of the derivative?
 2009-06-10, 14:05 #3 ATH Einyen     Dec 2003 Denmark 343910 Posts 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
2009-06-10, 19:26   #4
hallstei

Apr 2005

D16 Posts

Quote:
 Originally Posted by ATH 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

2009-07-02, 20:56   #5
flouran

Dec 2008

72×17 Posts

Quote:
 Originally Posted by hallstei 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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