Hello All,(adsbygoogle = window.adsbygoogle || []).push({});

I was hoping one of the many knowledgable people on this forum could give me some helpfull advice on how to proceed with the following problem. Basically, I am trying to fit experimental data to a curve.

In general my curve looks like this and I know the constants have the following constraints. I also know the range and domain of the function over the area I am interested in.

f(x)=a*(x^2)+b*x+c,

0<=f(x)<5, 0<x<50, -1<a<0, 0<b<1

I have never seen a negative c and I think the following should hold, |a|<|b|, but I would rather not rely on either if possible.

Oh ya, this is probably obvious but just in case, x is the variable I can control well and f(x) is the measured value. Also, I can vary x over the entire domain given and take many measurements. a, b, and c are constant for one particular setup but will change when I physically change the setup (i.e. switch to new components).

Anyway, this system is linear and quite easy to deal with. Unfortunately this is a sort of a reduced setup. I'll call it Experiment 1. What I really want is Experiment 2 which changes my characteristic equation to:

f(x)=a*(x+p)^2+b*(x+p)+c

Unfortunately I cannot control p or measure it directly (actually if I change to an experiment 3 I can, but there are good engineering reasons to try to avoid doing so. It is also a lot of work and this experiment needs to be repeated many times for different setups so time spent here could result in significant time savings overall) Anyway, I do know its possible range, 0<p<2.

The other constraints still apply. Oh ya, p will be constant throughout

the setup as well.

I believe this system is non-linear (because two unknowns are multiplied together) and I know there are iterative methods to solve such a system but I know very little about them.

I am sure this is a solved problem. Does someone know the name of the solution or technique to solve it? I did do a little googling before writing this post and found some info on root finding. Is this a good technique to try? Perhaps there is some nifty variable substitution I am not seeing that could reduce this to a linear case?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help Solving Non-Linear System

**Physics Forums | Science Articles, Homework Help, Discussion**