Setting up fixed point problem
- To: mathgroup at smc.vnet.net
- Subject: [mg42822] Setting up fixed point problem
- From: "Mark S. Coleman" <mark at markscoleman.com>
- Date: Wed, 30 Jul 2003 04:07:59 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Greetings, I'm working on a problem involving estimating the parameters of a fairly complex probability distribution. Denote the vector of parameters by x. It has been shown that the following "fixed point" equation provides a solution f(x(i+1)) = f(Sum[x(i)]} + v where v is a fixed vector of size conformable with x, and where i denotes the fixed point iteration (i=0,1,2,...). In this case the function f is the digamma function, denoted PolyGamma[] in Mathematica. I have two questions. First, can this be set-up using the built-in FixedPoint[] function, and second, can the digamma function be inverted in a straightforward way to yield the value of x at iteration i ? Thanks! Regards, Mark