fitting parameters to a differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg108398] fitting parameters to a differential equation
- From: eric g <eric.phys at gmail.com>
- Date: Tue, 16 Mar 2010 04:46:43 -0500 (EST)
Hello Group,
does this make sense to you?:
Suppose I have an second order differential equation on y[t]:
y''+ay'+by=0, and I have a noise measurement of {y[t], @t1,t2,....tN}, I
would like to fit 'a' and 'b' using the differential equation rather
than using the solution.
I will proceed like this:
* take my y[t1],...,y[tN] measuremenst and do b-splines interpolation (I
dont know what is the best way to do this), named yi[t], then find
yi'[t], and yi''[t]
* then I have an algebraic system on 'a,b' with N-equations (N is a big
number) ayi'[t1]+by[t1]=-y''[t1],.....
* how to use pseudoinverse to fit 'a' and 'b'? do you think this way may
be better that a nonlinear fit (weighted nonlinear regression) using the
solution of the equation? Do you think that this way may avoid the
problem of finding the appropriate guess for the nonlinear fits
algorithms with is ussually an issue?
best regards,
Eric