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Article #1012

Aproximating a messy product ...

#1012
From: Levent Aydin
Date: Mon, 04 Jan 1993 23:25
25 lines
1555 bytes
	Hello everyone;
	I need to approximate a function given in terms of a product with a
simple function that I can deal with.The expression is as follows:

               n              /            \  
              __             |    x-m_i     | 
        g(x)= || 0.5*{ 1+ erf| -------------| }
              i=1            |  sqrt(2)*s_i | 
                              \            /  

	Here, m_i and s_i are two known sequences of non-zero real numbers.You 
can assume that the sequence m_i is a descending sequence and the value of s_i is
directly proportional to the value of m_i for each i.Also it is known that the
sequence m_i is such that it has only couple values which are significantly
larger than the rest of them.
	So far all I could figure was that the product is determined by the terms
with large values of m_i.I think that the product can be approximated by a
function similar to one of those terms, i.e. 0.5*{1+erf[(x-mo)/(sqrt(2)*so)]}.
The question is what are the optimum values for 'mo' and 'so'.
	Any input will be greatly appretiated.Thank you very much...


							L  E  V  E  N  T
P.S: The function erf(x) is the standard error function.
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Path: arc1-ca.pugleaf.net!sparky!uunet!usc!laydin
From: laydin@solar.usc.edu (Levent Aydin)
Newsgroups: sci.math.num-analysis
Subject: Aproximating a messy product ...
Date: 4 Jan 1993 15:25:03 -0800
Organization: University of Southern California, Los Angeles, CA
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Message-ID: <1iah0fINNjhj@solar.usc.edu>
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