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Topic: Computationally efficient method of assessing one measure of
variation of a function

Replies: 2   Last Post: Feb 24, 2013 9:41 PM

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Paul

Posts: 464
Registered: 7/12/10
Computationally efficient method of assessing one measure of
variation of a function

Posted: Feb 22, 2013 4:43 AM
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Let N be a positive integer. Let f be a function from the nonnegative integers <= N to the reals. Let d > 0. What is a computationally efficient way of finding the largest possible k such that there exists M >=0, M + k <=N
such that abs(f(x) - f(y)) <= d for all x, y such that x and y are both >= M and <= M + k?
I'm also interested in continuous analogies. For example, suppose f is a continuous function defined on a closed interval. How do we find the length of the longest interval I in the domain of f such that abs(f(x) - f(y)) <= d whenever x and y both lie in I.

Thank you,

Paul Epstein



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