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Running Maximum


Given a sequence of values {a_k}_(k=1)^n, the running maxima are the sequence of values {max(a_1,...,a_k)}_(k=1)^n. So, for example, given a sequence (3,5,7,8,8,5,7,9,2,5), the running maxima are (3,5,7,8,8,8,8,9,9,9). The unique values of the running maximum are sometimes known as high-water marks, so the high water marks for the above sequence are (3,5,7,8,9), which occur at k=1, 2, 3, 4, and 8.


See also

High-Water Mark, Local Maximum, Maximum

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Cite this as:

Weisstein, Eric W. "Running Maximum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RunningMaximum.html

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