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MathGroup Archive 2007

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Optimizing inverse functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82981] Optimizing inverse functions
  • From: Teodoro <jwheeler51 at gmail.com>
  • Date: Tue, 6 Nov 2007 03:38:15 -0500 (EST)

In a previous post I said that I'm tring to find a general way to get
the Gommel-Poon parameters of a BJT. To do so I needed a way to invert
functions like
f[y_, m_, p_, n_, q_, r_] = m Exp[p y] + n Exp[q y] + r
A good way to do so is to write:
g[x_, m_, p_, n_, q_, r_] =
 Reduce[f[y, m, p, n, q, r] == x, y, Reals][[2]][[2]]
Now I need to proceed further.
Let us assume we have for g[x, m, p, n, q, r] "measurements" like
{1.3,2.88289*10^-7},{2.1,2.8829*10^-7},{3.2,2.88292*10^-7},
{4.5,2.88293*10^-7},{5.3,2.88295*10^-7},{6.1,2.88296*10^-7},
{7.3,2.88297*10^-7},{8.2,2.88299*10^-7},{9.4,2.883*10^-7},
{10.1,2.88301*10^-7}
What is the best way to find [m, p, n, q, r] ?
The result should be:
m = 7.984136668700428*10^-14; p = 38.64734299516908; n =
 9.185777*^10 - 7; q = 7.729468599033817; r = -9.18579746734159*^10 -
  7;
Unfortunately the "real" problem is full of "fake" minima ...
Thanks
          Teodoro Marinucci



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