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Article #1012Aproximating a messy product ...
From: Levent Aydin
Date: Mon, 04 Jan 1993 23:25
Date: Mon, 04 Jan 1993 23:25
25 lines
1555 bytes
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 Lines: 25 Distribution: world Message-ID: <1iah0fINNjhj@solar.usc.edu> NNTP-Posting-Host: solar.usc.edu