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multiple argument MIN function?
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| Serhiy Kosinov 2005-03-23, 4:01 pm |
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Dear All,
a binary MIN function can be written as:
MIN(a,b) = 0.5*(a + b - abs(a-b))
Does there exist a multiple-argument version of MIN?
That is, can MIN(a_1, a_2, ... , a_N) be expressed in a non-recursive flat formula that involves its arguments and absolute values?
I need this for a smooth differentiable minorizing approximation of MIN obtained by replacing abs(x) with sqrt(x^2+delta), for a given small positive delta (~0.001 or something like that).
Thanks in advance.
Serhiy
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| Penny Anderson 2005-04-20, 9:00 pm |
| "Serhiy Kosinov" <kosinov@cui.unige.ch> wrote in message
news:4241ba1c$1@nntp.unige.ch...
>
> Dear All,
>
> a binary MIN function can be written as:
>
> MIN(a,b) = 0.5*(a + b - abs(a-b))
>
> Does there exist a multiple-argument version of MIN?
> That is, can MIN(a_1, a_2, ... , a_N) be expressed in a non-recursive flat
> formula that involves its arguments and absolute values?
>
> I need this for a smooth differentiable minorizing approximation of MIN
> obtained by replacing abs(x) with sqrt(x^2+delta), for a given small
> positive delta (~0.001 or something like that).
>
> Thanks in advance.
>
> Serhiy
Serhiy,
min( [ a_1, a_2, ..., a_N ] )
should do the trick.
Penny Anderson
The MathWorks, Inc.
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