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Re: midpoint, slitpoint

On 05/12/2012 11:05 AM, John Pryce wrote:

Arnold

On 11 May 2012, at 20:20, Arnold Neumaier wrote:

On 05/11/2012 06:21 PM, Jürgen Wolff von Gudenberg wrote:

P1788
what do you think of the proposal to define the bisect operation with
the splitpoint as a parameter ? then eithr midpoint or flmean or any
interior point can be used.
If we offer a default, flmean seems to be a good choice


There is no good default.

flmean has serious deficiencies for splitting [0,1],
while the midpoint has serious deficiencies for [1,1e12].


Can you elaborate? What is flmean's deficiency over [0,1]? I don't think anyone has given a precise spec of an flmean that removes the exceessive bunching of numbers near zero, so your answer may clarify.
With flmean I refer to the vanilla algorithm that returns the median of the floats in the interval. (This simplicity makes it suitable for standardization.) [More precisely, it should be called flmedian]
If a function is defined on [0,1], splitting at the flme(di)an will result in splitting off repeatedly very tiny intervals, and thus waste efforts on all but very pathological functions.
Thus flme(di)an has the same sort of problems near 0 that the midpoint has near Inf.